score:2
There is a bus line especially for that (crossing the border and connecting the two networks), called MWR for Mouscron-Wattrelos-Roubaix. As you suspected it does not go to Tourcoing but to Roubaix, where you can connect to the metro and the rest of the Lille area transit network. The problem is that the last bus service is even earlier than the last train.
Since the line does exist but does not operate so late, I think it means the only option left is walking (or perhaps a taxi?) There is also a high-service bus to Wattrelos (called βLiane 3β) that runs quite late in the night. It does not go over the border but the walk from Mouscron (Herseaux station?) could be shorter (apparently a bit over 2 km on the map). I have never been there with public transport so I don't know how realistic this option is.