First, keep in mind that you're asking for free advice, so posting with an attitude isn't always conducive to getting helpful responses. Secondly, the quality of the responses is based on the amount of information you give in your post. Belittling anyone for not "asking you about your status" isn't going to help.
Any temporary residence application is processed on the assumption that you intend to stay in Canada - i.e. you have to prove the officers wrong. They look for ties to your home country (property, financial assets, family, etc.) - they more ties, the better. With your wife studying in Canada, this just gets more difficult for you. If you own a house in France, then including a copy of the deed will help (or other long-term assets, including cars, etc.).
As I said in my first post, you could potentially be eligible for an open work permit through your wife's study permit (see http://www.cic.gc.ca/english/study/work-spouse.asp) - it will be valid for as long as your wife's study permit is valid. As such, if you can gain your post-doc experience on the work permit, then I'd highly suggest going that route as you won't have to demonstrate as many ties to your home country since it is inherently linked to your wife's status.
