It isn't a weird rule. Most countries (including Canada) have limits on how long a tourist can remain without a visa, and 90 days is quite common.
You can spend up to 90 days in the Schengen area in any period of 180 days. The 90 days doesn't have to be consecutive, and the clock starts again after every 180 days. The Schengen area covers most of the EU except the UK and Ireland, and as it happens the UK will let you stay for up to 180 days consecutively. So as I understand it you could visit Europe virtually indefinitely by simply dividing your time between continental Europe and the British Isles. The same trick is possible by visiting some Eastern European countries which are also in the EU but not in Schengen - you can google for them.
this doesn't help you much with living in France, of course. If you want to do that, then your desire to attend a language school might be the answer. Make enquiries about a student visa.
As for touring in France, the possibilities are endless. It's hard to think of a part of the country I wouldn't recommend. But if you like the mountains, the French Pyrenees might be to your taste. Wherever you choose, please eat in French cafes and restaurants. It hurts me to think of anyone touring in France and eating McD's, really.