Popular belief has it that the "Old French" title derived from a remark by an old Vermont fiddler who, when asked its title, said it was "just an old French tune." The reel was known in Canada prior to the "folk revival" that fed American contra dancing, and was in Maritime fiddler Don Messer's "Down-East" repertoire (probably the source for the American "revival" musicians).
The original provenance is in Québécois repertoire, where it was recorded in 1929 under the title "Reel de St-Tite" on a 78 RPM recording by Sotère Mongrain and Ida Mongrain (violin with piano accompaniment). Ottawa Valley fiddlers know it as "Rambler's Hornpipe" or "Little Old Man," while Cape Breton fiddlers call it "The Old French Reel".
I learned this initially from some print source that I have forgotten and later relearned it from our Monday night jam list.
I don't usually play this on the banjo so the banjo tab is from Ken Perlman's Melodic Clawhammer Banjo (1979). Ken plays banjo a little like classic guitar and frequently uses off-string pull-offs that have always given me trouble. This is a really nice banjo arrangement and some day I will learn to play it.