I've moved your post into a thread of its own in hopes of stimulating a bit more discussion.
First question is, of course, what sort of visa are you planning on getting for the move? If you are hoping for a work visa (i.e. employer sponsored), it will be very tough going. Basically, there are more than enough native English speakers willing to teach English who don't need a work visa, so you'll be at the end of a long queue.
If you have another sort of visa that gives you working rights (spouse visa, student visa, etc.) then your best bet (at least at first) might be to post notices in the local bakeries, butcher shops and other public message boards to try and attract some freelance clients. There's definitely a market in tutoring lycéens for their exams in English. And, of course, hit the local language schools to see if they have posts or contract work available.
ahhh there it is - I got a notification on our thread but there was nowt there...sneaky Bev!
I teach English privately (with an organisation) but even they struggle to get businesses on board and at the moment my student numbers are down due to budget tightening. BUT I believe if you are happy to do the ground work you can build up a good amount privately by advertising online (leboncoin) and getting your information out and about. The only restraint may be trying to get people (if you are teaching kids) to book outside of a Wednesday - as this is the day EVERYONE wants due to the schools being closed in the afternoon...so the kids are free... so my answer is yes it can be done but it could take some time to build up a network (would rather be honest on that score!) IF you do move here I would happily recommend you to people that enquire