I am an auto-entrepeneur, writer, photographer, researcher, coach, historian and we run a chambre d'hote/activity centre
It is v easy and uncomplicated in terms of declaring income
The main problem I found was that I left Engineering and Manufacturing (Project Manager) and took some time out to run a shop for my neighbour in the UK. Then when I came to France I did the same for a while but it just wasn't the same, so I decided to try and get back into Engineering. The problem being that the French companies don't like it when you've changed direction once or twice regardless of the fact that I was using more or less the same skills, just with different products. They love to label people over here and you have to really prove that you can cope. Also, totally agree with Barrie, the language is an absolute must. Although I probably have a limited vocabulary, being from up North like eh, I speak reasonable French with not too much of an accent. Can be a disadvantage though, when people think you know every word in the French dictionary.
So, in a nutshell, speak French, do your homework on the company or the product, enough to bluff you through the first three months and Bob's your uncle.
If you want to be self-employed no problem for being employed - learn french....
We both work in France, my husband is a self employed metal worker, making things like staircases, gates, fences, pergolas and much much more! while I have 2 jobs: firstly as a writer (for an English company but with content based on France)and the second as an English teacher (I qualified many years ago while still in the UK to teach ESL) both in lycee and privately. Best advice? Find a gap in the market before you move, if possible ...it is very hard to find a salaried position unless you have particular skills that are impossible to find among the local population. If running your own business, be prepared for LOTS of paperwork!!!