Chicken French is not a commonly found term for this cooked specialty outside of the Rochester, or Western New York State area, although Veal French is cooked in in similar way.
Commonality among the recipes is pan-fried boneless chicken, with flour, egg, lemon, Sherry, often additionally butter and chicken broth, and making a gravy which then is put on the chicken when served. Other additional spices found in some recipe variations.
Recipe is similar to the Veal French recipe, with variations such as artichoke french, and seafood versions.
This is very often not the same as the French Chicken recipe found in many cookbooks.
Wikipedia entry on Chicken French
1885 Sutherland House, Canandaigua NY - Recipe on 1st Traveler's Choice internet cookbook