How do you get to the border? On a train!

You don't actually have to get off at the border - you just get on a train that crosses the border. Border crossings are charging points for rail travel. If you travel between Country A and Country B and you have a railpass for A but not for B then you use your railpass for travel to the border and buy a ticket for travel from the border to your final destination. If you have railpasses for both countries then you don't have to do anything - you just get on the train with your two passes.

If time is short you could always fly to Prague instead of taking a train... there should be some cheap deals to be had.

As for flying vs the train between London and Paris - depends what your starting point is. If you want to go Paris immediately after arriving on a long-haul flight (i.e., without going into London), AND you can get a flight from your long-haul arrival airport (LHR or LGW), then flying makes a lot of sense. If your starting point is Central London then the train makes more sense.