Not a whole lot, at least in the early years. The problem is that the Angevin empire doesn't really fit into the modern perception of what "England" is. It's less helpful to think of the Angevins as being "English in control of French lands" as it is to think of them as "French lands in control of England". They tended to be French dukes of Aquitaine and Normandy first, and English second; the famous "English" king Richard the Lionheart spent less than two years of his life in England, and couldn't speak English himself! This also explains the influence of French on English, in that the nobility tended to speak French or patois, and so it took on the status of a prestige language. It's much more difficult for English to permeate into the French regions, since they would have been administered in French, by French-speaking (if not always French) nobility. We do see occasional references or borrowings from English, but these rarely survived to become part of the actual vernacular. Dogue, meaning "dog", and estrope, meaning "rope" are examples of these, which to my knowledge haven't survived into modern French. Nautical terms such as écore, from "score" (shore) and héler, from "to hail", as well as militaristic terms such as haquenée, meaning hackney, were most common. Of course, the English soldiers brought in "goddam" or "godon", both corruptions of "God damn", and that remained a legacy of the Angevin presence long after they left. It was primarily used to refer to the English themselves as a pejorative, however, so it may or may not really count. By the time the English were cast out definitively in 1453, most of the transient influences of English on contemporary French had passed.

Even so, the 18th and 19th centuries saw a certain amount of English borrowings in French. This has been described as "Anglomania", and was precipitated by the growing influence of English philosophers and playrights on the French tradition, particularly Voltaire. It also coincided with a large influx of English nobles making France something of a holiday destination, to the extent that Paris often resembled modern Marseilles in the summertime. This was much, much more significant than the phenomenon seen when the "English" actually controlled France. In this we see words such as baby, whiskey and all-right transmitted as bébé, whisky and olrède respectively. Where originally we saw borrowings mostly from the naval and military sectors, these new borrowings were found coming from and into all areas of society. French nobles would don a redingote to go riding, or bowl on a boulingrin. Predictably, this prompted much complaint from French nationalists; even Voltaire, who largely began the trend, bemoaned the introduction of English, comparing it to "a pile of manure" introduced into the French language. In fact, many of the English words that were "introduced" into French, actually originated from French in the first place, but had fallen out of favour in the interim. "Sport" and "verdict" are both direct loans into French from this period, but originated from Old French as desport and veir dit. This is also the period in which the term "rosbif" for the English arose; the English were so associated with the roasting method of cooking meats that the French came to identify them with it. If I recall correctly, beef, "bif" and boeuf have some amusing linguistic gymnastics in their history, but I'm not 100% on that; I'll have to check before spouting something I may have completely wrong. In terms of actual linguistic intercourse, the Age of Englightenment was much more significant than the Hundred Years War; English was a prestige language in the former, and not the latter, which is better framed in many respects as a war between Frenchmen than a national conflict.

Edit: Couldn't find the book that had the story of beef, so I won't go into that. It did come from French in the first place, then made its way back in the corruption "bif", but beyond that I'm a bit fuzzy.

Could you clarify what you mean by English controlled areas in France? The wording of your question implies, at least to me, a sort of nation-state conception of the relationship between the Kings of England and their lands on the continent. Prior to the Treaty of Brétigny that ended the first phase off the Hundred Years' War, the King of England possessed lands within the Kingdom of France as a vassal of the King of France. That is, Normandy was not an English possession, the King of England simply happened to be the same man as the Duke of Normandy, and the Duchy of Normandy was legally a part of the Kingdom of France. While acting as Duke of Normandy (or Count of Anjou, or Duke of Aquitaine), he was legally a vassal of the King of France, and the Kings of England, in their capacity as Dukes of Normandy or what have you, often had to pay homage to their liege. The fact that the King of England (equal to the King of France) could simultaneously be a duke (vassal to that same king) was a point of contention between the two monarchies for quite some time before the Hundred Years' War. It was not the same as Normandy or Aquitaine being a part of England.

Side question; how much influence did English language and culture have on port cities on the continent side of the north-sea such as Calis, Antwerp etc?