A simpler explanation is that people tend not to be able to hear their own accents.

Someone who wasn't brought up speaking French will probably never have an "absolutely perfect" accent. They may think that they sound exactly like everyone around them, but to someone brought up speaking French, they don't.

There are a lot of British actors who do American accents for various parts. These are native English speakers who grew up listening to American accents on TV shows and in movies. They work with dialogue coaches, and can rehearse their lines until they think they can deliver them perfectly in American-style English. Any slips in their accent can be fixed in ADR before the film is released. Yet, many people, including me, are able to spot a few quirks in their speaking and often identify these people as not American.

For French in particular, it has the "u" sound that also exists in German, but doesn't really exist in English. Many people who weren't brought up with that sound can't even really hear it, or can't hear it as different from the "oo" sound that they associate with the letter "u". As a result, words like "ouverture" don't have two distinct "oo / u" sounds for them. So, they might think they're speaking flawlessly and that nobody can notice, but it's really obvious for anybody who was brought up hearing and speaking French.