It happens that the French Suites of Bach are not really French at all ( just like the French horn is German, and the English horn is neither English nor a horn. It’s thought to have originated in Silesia, which is an area now predominantly in Poland). The word “french” attached to these suites did not appear until 12 years after Bach’s death.
A few of the individual dance movements are French in character – Bach merged the French, Italian and German styles in these keyboard works. The French ones have that strong dotted rhythm and fast notes rushing towards the downbeat. Perhaps these were given the title “French” to distinguish them from the previously published English Suites (which are – wait for it – more French in style than the French Suites!) Dances of the same name in different suites vary quite dramatically.
This kind of fascinating information can be found by actually reading those liner notes of CDs – in this case, in the CD of the French Suites and Little Preludes that I bought at the Angela Hewitt recital last week.