The router will (should) have a log of all connections since it's last reset. That said, if it's the router a reboot will likely fix it.
Get scientific - ping the router and ping google when the internet seems fine to you and make a note of the times. Then next time your connection bottoms out, repeat the test.
If the time to ping the router is much slower, the the router or your computer, or the local network is probably the problem. If not, its outside your local network, and you should contact your ISP. If the ping to google is slow, a traceroute might tell you where the problem is (likely your ISP). If ping to google is fine when connection to blazzard is bad it might be something between your ISP and Paris, in which case they might not be able/willing to help.