… You know, I’ll take the challenge.
I have a PhD in linguistics and I know the IPA backwards, but my accent in foreign languages is horridly Greek.
Don’t assume that polyglots always have a great accent. I know a polyglot prodigy who has recently showed up on this site, so I won’t name him: he knows a dozen languages, and he sounds Bulgarian in all of them. You have to be immersed in a country for a fair while to pick up the accent with some fluency.
As both other answerers have pointed out, there would be shibboleths. The uvular [ʀ] would end up a velar [ɣ] or a trilled [r] (the former is likelier unless the speaker had never heard anyone speak French). The rounded front vowels, the [œ, y], would be way too close to /e/ and /i/. They’d have trouble with the [ɥ]. (Doesn’t everyone?) I think they’d do a passable [ʃ, ʒ], but their nasals would be hit and miss. And of course, they’d have the rat-tat-tat of a language without vowel length distinctions.
You know how Spanish speakers speak French? It’d be close to that.
, Linguistics PhD candidate at Edinburgh. Has lived in USA, Sweden, Italy, UK.