The course of the Tour de France change every year so, time to time, it might start in neigbouring countries. However most of it is raced in France and it has always finished in Paris.
Tour de France basically means "journey through France", so it can't really be held anywhere else.
There's another fairly well known competition that's called "Giro di Italia", which, guess what, is...
Depends on what you mean. There really aren't any countries competing, that's all done by professional teams that only represent themselves and are composed of people from all over the place. The...