Cotillard mentions how she worked very hard on improving her American accent for a role and then she says that the problem with learning English in France is that it is taught by French teachers. She says a few words in the “very French” accent of such teachers to show how bad it is
However, to my ears that “very French” scent is much more pleading than Cotillard’s current Americanish-but-not-quite-American accent. It falls into a kind of uncanny valley to me – too close but not close enough.
I can’t tell from that clip whether I agree with you about her accent specifically, but I can think of another example that may or may not be the kind of thing you’re talking about. There are at least a couple of people—Bill Bryson and Andrew Solomon—whose voices grate on me when I try to listen to them. These are people who have spent substantial portions of their lives both in the US and in the UK, and I suspect that at least part of the reason I find them so unpleasant to listen to is that their accents are a weird mixture of, or fall in an uncanny valley between, British and American accents.