I lived in Aix before moving to Spain for 18 months. It's a beautiful part of France (really stunning) however I never felt like I could live in France for my whole life due to the people there. I don't like the typical French character. I do howver now find myself in Ecuador teaching English online and running my English teaching company.
FInding work as a non-native speaker will depend on your belief and your level of English, grammar knowledge, confidence, experience etc. I think belief is the biggest thing and if you have that you can do it, definately. A friend of mine in Pamplona was Dutch and he taught in a school and he'd make the odd grammar mistake.
For my English teaching school I'd only take on native people but I know there are many schools who'd welcome non-native persons.
All the best.