London Underground trains don't go to France. Do you mean the Eurostar? If so DTG don't have a license with them so they couldn't produce the required units. Closest they could do right now would be to make HS1 and run the javelin's down it, BUT I don't know if they have a license for the Kent stretch of that else they might have done it already
I can't say it would be the most exciting route ever. Maybe the section of Eurostar before the tunnel could work, but not the actual tunnel.
Given that St Pancras to just outside Stratford is all tunnel I don't think it would be too much of an issue Also there are a few interesting points in the tunnel itself (I'm thinking the cathedral cross overs for one) I believe at top whack the Eurostar would be in the tunnel for about 20 minutes but I don't think there are any speed changes so it would literally be set your speed and wait...
Tunnel could be interesting with train management on the gradients, especially for a heavy freight, but that's all. Being single track bores you wont see any AI, and even the crossovers are closed off with fire doors when not in use.