The Chicago Manual of Style holds that adjectives that refer to a nationality or a place are usually not capitalized when used in a nonliteral way; thus dutch oven, french windows, and venetian blinds.
I came across French drains in a book I was copy editing today, and I very nearly lowercased it out of habit when I realized I had no idea what a French drain was. Was it possible that a French drain was in some way literally French? I couldn’t imagine a way that it could be, but I stopped to Google it just in case.
Wikipedia asserts that some authorities say the term is “merely a popular corruption” of the term trench drain (which is a real term, though for a slightly different kind of drain), in which case it would certainly be lowercase f. But I decided to keep looking anyway, and a good thing I did, too, because over 100 other websites — including Wiktionary — say that the French drain was invented by Henry French of Concord, Massachusetts, who published the idea in his 1859 book, Farm Drainage.
I haven’t actually searched the Library of Congress database to confirm that such a book exists, because life is short and so are deadlines, so it’s not impossible that the existence of this book is merely an urban legend. But given the specificity of the references, and the fact that a couple of the sites contain some details as to Henry French’s biography and the contents of his book, it seems much more plausible to me that the French drain/trench drain connection is the popular mistake and that Henry French is the correct explanation. So till I learn otherwise, that’s the one I’m going with.
Ergo, capital F.
Later: Dave found copies of the book listed for sale at Bookfinder, so I think that closes the case. Farm Drainage seems to have been very popular: it went through many editions and was still in print in the early 20th century.