Captain Picard (a Frenchman), is so obviously English throughout the run of Startrek TNG. He speaks with an English accent and spends his time drinking tea.
There's also several times in TNG when French is referred to as an archaic language. Picard was fluent, but even he gave himself away as a nonnative speaker despite actually growing up in France. It doesn't appear to be because humans have chosen a unified language, either, since several characters like Chekov have vocal quirks that give them away as nonnative English speakers, so at least some non-English languages are still in use.
Whatever happened to France, it was fairly recent, very late 23rd Century or first half of the 24th. It was still a contemporary language in Enterprise, and there was a French-speaking colony in TOS.