Was Geoffrey Plantagenet English or French?

This is an interesting question with several possible answers depending on which Geoffrey Plantagenet we are interested in. You might be referring to Geoffrey Plantagenet, the originator of the name "Plantagenet," who was the husband of Empress Matilda and the father of Henry II of England. You might also be referring to Geoffrey Plantagenet, the son of Henry II and the grandson of his namesake. Let us begin with the assumption that this question is asking about the older Geoffrey, Count of Anjou and the first Plantagenet.
Geoffrey Plantagenet, Count of Anjou, was called "plantagenet" because he was said to wear broom ("plante genet," or "yellow plant") on his person. He was the son of a count of Anjou, had a French mother, and was, all in all, decidedly not English. He was born in France at a time predating the massive expansion of the kings of England into that area and had no reason not to consider himself French. He was sought out to marry Empress Matilda, the heir-apparent of Henry I of England, because of his reputed talents. As a result, he became the father of one of England's great kings, Henry II.
Whether the younger Geoffrey Plantagenet was English or French is a more complex question. He was born to a king of England, but that king, Henry II, had spent most of his life in France until he acceded to the throne. Moreover, the monarchy of England at this time was, effectively, French. Indeed, their first language was French, and their associations with nobles in France was such that Geoffrey was best of friends with the French Dauphin, Philip Augustus. His mother, Eleanor of Aquitaine, was also French. Although living in England and heir to the English throne, the younger Geoffrey Plantagenet was born to a French mother and a French-speaking father descended from Normans who was also the Count of Anjou and ruler of much of France. Were they French or English? At this time, England was arguably a country living under the rule of a French aristocracy.