While pursuing one of my useless college degrees, I learned that accent in a foreign language is influenced by many factors. The age at which one learns the L2, for example, is very important. Generally speaking, if you learn (really learn, not just get a little exposure to) a language before puberty, you won't have an accent. After that, you are pretty much guaranteed to have one. (Part of the very famous Critical Age Theory.) The status of the minority language is also important. A study conducted in US airports revealed that non-native English speakers with French and Italian accents were treated much differently than those with a Spanish accent (so an Italian man, for example, has little motivation to 'lose' his accent, given that it is seen as attractive). Other factors include, but are not limited to, extent of cultural and social integration, education level, professional activity, presence of a 'musical ear', fatigue, recent dental work, etc.
Those of us who are non-native speakers of a language show it in a variety of ways. There's accent, of course, but also (and not limited to) non-native syntactic constructions, approximative vocabulary, lack of fluidity or 'fluency', surface grammar errors like wrong gender, faulty verb conjugation, etc. Bored yet?
Beth was not that far off the mark in her comment to yesterday's post. I don't have much of an accent when I speak French, at least not all the time. (Although I don't think that's why I'm introduced as American.) And so, sometimes, people don't pick up right away on the fact that I'm a non-native speaker. But that is not necessarily a good thing.
Picture this. I'm alone at the farmer's market. (Alone matters because if the kids were with me, my foreignness would be obvious as soon as I spoke to the kids.) I go up to a stand and ask for, with no discernable accent, a couple of things. I chat with the farmer, and then I decide I want an onion. I ask for une oignon. The farmer looks at me like he's not quite sure what on earth is wrong with me. Yes, everyone knows it's un oignon. And native speakers never make gender errors, gender is inherent in the word for them and the article is just the external marker for it. Whereas for non-native speakers, gender is just another thing to learn and remember. Anyway, at this point, I reassure the farmer by telling him I'm not French. Ah, d'accord. I am then, usually, given deferential treatment and thanked profusely for stopping by. But sometimes I don't have the time to explain or don't want to. Which means that after having made a glaring grammar mistake, I just leave them with impression that I didn't make it out of primary school.