Hi,
I didn't take any of the test, but my mother is in charge of the TOEFL training in her university, so I got to test it for it for fun. It seems that the TOEFL is the test preferred by universities, as it mostly focuses on grammar, whereas the TOEIC is more field-specific, and thus more likely to be required by a company. Though it is subjective. I expect you'd have to have a very good TOEFL score for a job which required you to write in English.
As for the IELTS, from what I know, in France only students applying for masters in the States take it. Hope I was of some help.