Depends on what mode of transport you want to use - driving would take a day, but there are probably flights to within a couple of hours, eg to Toulouse from Edinburgh Airport.

I think driving would take rather more than a day -- from Edinburgh down to London, around the M25, down to Dover, onto the boat (or train through the tunnel), and then the length of France. That's a long day's drive, if you ask me.

You could fly Edinburgh - Paris and take the train across France from there, perhaps. As lonaK says, it depends on how you prefer traveling, how much time you have, and whether you want to see anything on the way.

have you tried hipmunk?