If you've ever wondered how a fourteenth-century king of England (born in Wales) came to inherit a county in northern France from his Spanish mother - and be honest, this vexatious question has been keeping you awake at night, hasn't it? - here's everything you need to know. ;-)
The county of Ponthieu no longer exists on the political map of France; it is part of the region of Picardy and is located in the modern départements of Somme and Pas-de-Calais. Its main town is Abbeville and its former port (now inland) is Montreuil-sur-Mer. In Edward II's time and before, it was a small county with a strategic importance beyond its size because it bordered Normandy. The battle of Crécy in 1346 took place in Ponthieu, so Edward III was on home ground, as it were, having been granted the county by his father on 2 September 1325.
We're going to go back to 1195, when Alais (or Alix or Alys, etc) of France married Guillaume or William Talvas, count of Ponthieu. Alais was the younger daughter of Louis VII of France and his second queen Constance of Castile, who died shortly after her birth on 4 October 1160; Alais's elder sister Marguerite married Henry the Young King, son of Henry II of England and Eleanor of Aquitaine, who had of course once been married to Alais and Marguerite's father Louis VII and had two daughters with him. (I wonder how many married couples in history have had half-siblings in common.) Anyway, Alais was betrothed for many years to Henry the Young King's brother Richard Lionheart, but he refused to marry her and in 1195 finally sent her back to her younger half-brother Philip Augustus, king of France, on the (spurious?) grounds that she had borne a child to his father Henry II. Philip immediately arranged Alais's marriage to William, count of Ponthieu, and the couple married on 20 August 1195. Alais was then a few weeks short of thirty-five, William a youth of probably sixteen. He was the great-great-grandson of the notorious Robert de Bellême, a Norman baron who also owned lands in England and was imprisoned by Henry I in the early 1100s having committed all kinds of atrocities in Normandy; Robert's wife Agnes was the heiress of Ponthieu. A previous count of Ponthieu, Guy, Robert de Bellême's father-in-law, played a small but vital role in English history in the 1060s, when he imprisoned a shipwrecked Harold Godwinson and delivered him to Duke William of Normandy, later the Conqueror.
It is likely that Philip Augustus was hoping or expecting that Alais and William's marriage would remain childless so that he could gain control of Ponthieu, but a daughter, Marie, was born to the couple sometime between 1197 and 1199 when Alais was in her late thirties and William still probably under twenty (Marie's date of birth is sometimes given as April 1199). Marie was their only child, or at least their only child who survived to adulthood, and was thus the heir to Ponthieu when Count William died in 1221 (the date of Alais of France's death is unfortunately not recorded; I hope she found some happiness with her much younger husband after being publicly humiliated by her long-term fiancé). Marie married Simon de Dammartin, count of Aumale, and had probably seven children, of whom four daughters lived to adulthood. Marie and Simon's eldest surviving child, who was born in about 1216 to 1220 and was heiress to Ponthieu, was Jeanne de Dammartin, who is usually known as Joan of Ponthieu in English. In 1235 Joan was betrothed to Henry III of England, who hoped to use Ponthieu as a springboard to regain control of the duchy of Normandy, which his father King John had lost to the French in 1204. The regent and queen mother of France, Blanche of Castile, would not allow that, however, and threatened to invade Ponthieu if the marriage went ahead. Henry III married Eleanor of Provence instead, and Countess Joan married Queen Blanche's nephew the widowed King Fernando III of Castile and Leon in 1237. Henry III and Eleanor of Provence, and Fernando III and Joan of Ponthieu, are Edward II's grandparents.
Joan's father Simon de Dammartin died in 1239, having lived long enough to see his eldest daughter become queen of Castile and Leon, and her mother Marie, Alais of France's child, in 1251. Joan became countess of Ponthieu in her own right (one major difference between inheritance law in France and England is apparent here: in France the eldest daughter inherited everything, whereas in England the inheritance would have been divided equally among the sisters, the law of primogeniture applying only to males). Joan's husband Fernando III had had ten children with his first queen Elisabeth or Beatriz of Swabia - granddaughter of two emperors, the Holy Roman Emperor Frederick Barbarossa and the Byzantine emperor Isaac Angelos - and with Joan he had five more. Two, Juan and Ximen, died in infancy. The others were Fernando, who was born in 1238 or 1239; Leonor (or Eleanor), born probably in late 1241; and Luis, born before 31 March 1243. These children were the great-grandchildren of Alais of France and William Talvas.
Queen Joan was widowed on 30 May 1252 when Fernando III died in Seville, still only in her early or mid-thirties, and returned to her native Ponthieu in October 1254 following a dispute with her stepson Alfonso X over her dower lands, shortly before her twelve or thirteen-year-old daughter infanta doña Leonor married the future Edward I of England. Joan married secondly John de Nesle, lord of Falvy, and died on 16 March 1279 at the age of about sixty. Her granddaughter Joan of Acre, Edward I and Eleanor of Castile's second surviving daughter, had been living with her in Ponthieu, and returned to England on her grandmother's death. Joan's sons Fernando and Luis both predeceased her, so that her only living child in 1279 was her daughter, the twelfth of Fernando III's fifteen children, Eleanor of Castile, queen of England. On 21 March, five days after Joan's death, an entry on the Patent Roll gives "[p]ower to Edmund, earl of Lancaster and count of Champagne, the king's brother, and John de Brittannia, earl of Richmond, to exact from Philip [III], king of France, the king's kinsman, the county of Ponthieu, which by the death of Joan, queen of Castile and countess of Ponthieu, falls by hereditary right to Eleanor, the king's consort."  And thus the Spanish infanta and queen of England, lady of Ireland and duchess of Aquitaine succeeded as countess of Ponthieu in her own right.
Fernando of Castile, Eleanor's elder brother, had married Laure de Montfort, niece of the famous Simon de Montfort, earl of Leicester, brother-in-law of Henry III of England. They had a son, John of Ponthieu, who was born around 1264, around the time his father died. Eleanor's younger brother Luis, lord of Marchena, married Juana Gomez, lady of Gatón, but had no children when he died sometime in the mid to late 1270s. So at the time of Queen Joan's death in 1279, rightful posession of Ponthieu came down to either her daughter, Queen Eleanor, or her grandson, John of Ponthieu (whose fate it ultimately was to be one of the many French noblemen killed at the battle of Courtrai in July 1302). The daughter was preferred, though John of Ponthieu did inherit the county of Aumale, which had belonged to his grandfather Simon de Dammartin, and received 14,000 livres in compensation for Ponthieu from his aunt Eleanor in 1281. A daughter taking precedence over a grandson was not unusual in France at this time: Mahaut (1268-1329), daughter of Robert II, count of Artois, inherited the county on the death of her father in 1302 in preference to her nephew Robert (1287-1342), son of her dead brother, who spent many years unsuccessfully battling her for the county.
On Queen Eleanor's death on 28 November 1290, the county of Ponthieu passed by right to her only surviving son Edward of Caernarfon, then aged six. On 3 February 1291, envoys were appointed on behalf of "Edward, the king's son, lord of Ponthieu, with the consent and authority of the king as his guardian" to pay homage to Philip IV of France on his behalf, and on 21 June Edward I made a "[g]rant to Edmund [of Lancaster, his brother], the king's kinsman, of the county of Ponthieu during the minority of Edward, the king's son and heir."  Edward of Caernarfon lost his county from 1294 to 1299 when his father was at war with Philip IV and Philip seized English-owned lands in France, but in the Treaty of Montreuil of June 1299 - the same treaty which mooted his future marriage to Philip's daughter Isabella - it was given back to him.
Edward II remained count of Ponthieu until 2 September 1325, when he granted the county to his twelve-year-old son Edward of Windsor prior to sending him to France to pay homage for it and Gascony (i.e., what remained of the duchy of Aquitaine, which he inherited from his father Edward I and his great-great-grandmother Eleanor of Aquitaine) to Charles IV. And thus it came about that a Welsh-born king of England inherited lands in northern France from his Spanish mother, and thus it also came about that the discarded and humiliated fiancée Alais of France became as much an ancestor of the English royal house as Henry II and Eleanor of Aquitaine are. She was Edward II's great-great-grandmother. Richard Lionheart's brother King John was Edward's great-grandfather.
1) Calendar of Patent Rolls 1272-1281, p. 306; Hilda Johnstone, 'The County of Ponthieu 1272-1307', English Historical Review, 29 (1914), p. 437.
2) Patent Rolls 1281-1292, pp. 420, 435; Johnstone, 'County of Ponthieu', p. 447.