I did the old motorail service from Calais to Narbonne many years ago and it was very easy. It had to be booked in advance but once I arrived in Calais the process was very easy - a bit like the tunnel except you leave the bike and go into a normal bit of train. Next morning we got off at Narbonne and (eventually) got the bike back.
The current system, from what I understand, is a bit different - vehicles and passengers travel separately, so you could spend a day in Paris before catching a train or fly down to Nice or whatever. At its cheapest it could just about be worth while allowing for the cost of a (decent) hotel, fuel, tolls etc but tbh unless you really need to get your bike to Nice in a hurry it's not really far enough from Paris to justify the complexity. The terminal is right in the middle of the city and if you have to ride from Calais anyway you could be halfway to Nice before the bike's even loaded. It could save a bit of wear and tear I suppose and you could have a night in Paris before catching up on the TGV the next morning.
From the centre of London to the centre of Paris is going to take you about seven hours in the real world. It should be quicker but you'll always hit roadworks, just miss the tunnel booking in timeslot and get stuck behind someone who's broken down / lost their ticket etc
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