French TV websites are unfortunately geographically restricted. I have the exact same problem because I live in Belgium. However you can access them by using a French IP address. This solution is called VPN and uses a server located in France to access the content. This is unfortunately a paying solution. The less expensive I have found cost $40 a year.
A free solution is to use the browser plug-in "hola" (www.hola.org) but it seems not to work everywhere. With this plug-in, you can choose with a button which country is associated with a website. You have sometimes to change the server by clicking on not working in the menu.
The main French TV channels are :
TF1 :
http://videos.tf1.fr/ (live not woking with hola / catch up ok)
France 2 France 3 (France Télévision)(Public) :
http://pluzz.francetv.fr/ (not working with hola)
M6 :
http://www.m6.fr/ (catch up + live ok with hola)
Arte :
http://www.arte.tv/guide/fr/plus7 (live not working with hola / catch up ok)
Canal+ (Pay television with some free broadcasts) :
http://www.canalplus.fr/ (No VPN needed for catch up free broadcasts)
News channels :
BFM TV :
http://www.bfmtv.com/mediaplayer/live-video/ (no VPN needed)
itélé :
http://www.itele.fr/direct (no VPN needed)
euronews :
http://fr.euronews.com/infos/en-direct/ (no VPN needed)
france 24 :
http://www.france24.com/fr/tv-en-direct-chaine-live/ (no VPN needed)
With a VPN all works.
You can also use the application "captvty" to download broadcasts on those channels but you still need a VPN because some limitations can't be removed by the software. The application is legal but tv broadcasters fight against it.
If you want movies, series, tv broadcast you can use a French torrent website. You can find the most famous by searching "french torrent" in Google. The third results is what you want. The inscription is free. This solution is maybe not legal in your country, so use it at your own risk.