This is essentially a linguistics question. I recommend submitting to /r/linguistics.

Here are some words from Old English that have survived into Modern French. All were first cited in the 12th century unless otherwise indicated. I found these by searching for "ancien anglais" on larousse.fr and double-checking it in my French etymological dictionary.

• Nord, sud, est, and ouest (the cardinal directions) were all borrowed from English in the 12th century.
• Gourmet in French originally referred to a valet of a wine merchant (hence the association with the finer things in life) and was borrowed from an English word meaning "boy" in the 14th century.
• Mouette (gull) was borrowed in the 14th century from Old English, though the word was originally Frankish.
• A few sailing terms: bouline (bowline knot) and étai (support for a mast) from the 12th century, beaupré (a kind of mast) and arrimer (to stow, to tie down cargo) from the 14th.
• Loquet (latch) was borrowed from a Germanic source, possibly English, in the 12th century
• Paletot (a kind of long coat), 14th century
• Bréchet (a specific term for the breastbone of a bird) comes from the same root as brisket and was borrowed in the 14th century.