Sorry to reply that late... I let a few days pass to do some long-term testing and have a better perspective.
My overall connection quality improved a lot. According to Orange, they needed a bit of time to do the transition. So now I get 10Mb wired (instead of 3-5Mb before).
Concerning the wifi connection, it first went up to 6Mb only, but then I set the channel to 13 and now I get up to 8Mb (and a lot more stable).
The thing is, I still cannot connect to servers using wifi and I still have no clue what causes that.
As you requested, here are some screens of the wifi tab: