A technicien is supposed to be on top of ones field techniques, and know how to apply them. A techicien supérieur is the same but for more advanced and complex fields. An ingénieur is not only supposed to understand the "what" and "how", but also the "why" and be able to evolve things, of design from scratch when needed. That, of course, is the theory: there are plenty of techs with an ingénieur mindset (good), and unfortunately plenty of people with an ingénieur degree who couldn't innovate out of a paper bag.
BTS/DUT are short higher education degrees that focus on practical and professional skills, with selective admission (but not as selective as actual engineering schools). Basically in France you have: Grandes Ecoles ("great schools"), elite engineering schools that operate outside of the university system; you also have selective 2 or 3-year degrees inside high schools and universities (BTS, DUT, etc.) and then you have the universities. Where post-graduate degrees can sometimes be decent but undergraduate tends to be crap, and its pretty much a zoo or a jungle outside of STEM (fortunately, French universities tend to separate STEM campus from other disciplines filled with political activists).
You go work for a smaller company because they will hire you (and it will probably be more technical and less politics than the main companies)
All the main companies are headquartered in Paris (region) with some exceptions.
