did your provider SFR give you one of those combo modem + wifi built in?
if so a few troubleshooting tips for it would be to reboot it, even if its not a combo, reboot your modem and router.
If internet problems persist, i'd call their tech support and ask them to test your lines. they can see if theres a reason to your disconnects.
next up, make sure all your drivers are updated. personally i use Driver Magician and Driver Genius to make sure i'm current with all these items.
If you've got LoL installed, uninstall Media Booster, this robs you of internet as they use it to P2P their instal/update files. very shady practice as you're not even warned about this or have an option to say "no" to it being installed.
You want to keep CPU usage while gaming and streaming down to around the 80% and max usage at 85% peak. anything higher can cause a lot of drops in streaming, but not limited to the game starting to perform badly.
With your current kbps being 1,200 i'd highly reccomend dropping your resolution to 960x540, fps 30, and preset to very fast. in comparison to streaming at 720 vs 540, you should see a slight quality boost in the stream because theres more data packed into a smaller resolution.
this should put you in the area of using no more than 75 - 85% cpu.
i've got a few friends that live across the pond and they say their ISP throttles their internet, you can check using this guide
http://www.howtogeek.com/165481/how-to-test-if-your-isp-is-throttling-your-internet-connection/
the last thing, is search on google for "jtvping" some of your issue could be that the server you're streaming to has too high of a ping and/or jitter. this portable app will help you figure out the best server as your closest one may not actually be the best for your streaming needs.