I'm a bit surprised that you call it "Anglo-French" rationalism. I'd always associated the French with the continental tradition; the main names I know associated with continental philosophy are French. I'd thought it was called "continental" in explicit contrast with the British (and Anglophones in general).

Is there a large French "analytic" tradition that's getting swept under the carpet here?

I gather that the entire argument about the distinction is rather moot here. But I think I may also be missing your point entirely, and I'm curious if you could elaborate.