Have you ever realised that there are a lot of "foreigners" or foreigner-looking people that speak perfect English? For example, a notable one is Worf, having parents who have Russian accent, but himself having a Klingon-ish American accent. You might say this is a utopic (quite dystopic in my opinion) scenario where all of Starfleet speak the same way; but if you look at the characters, there are British characters who don't speak in American accent while no one in Starfleet uses Indian accent (Eugenics Wars, maybe because of that ':/). What I'm implying is that Worf speaks Russian (not Klingon, if he spoke Klingon, the translator would have corrected it to perfect English whenever he tried to speak Klingon) to his universal translator which translates it to perfect English; while Capt. Picard is actually speaking French which is translated to (perfect) English.
Anyways, this is not a very proper theory and it can be disproved, but it should make sense when you think about it.
Anyways, this is not a very proper theory and it can be disproved, but it should make sense when you think about it.