Yes, pursuing fight from French colonies was viable. The "proof" for that is that some of those colonies rallied to French Free Forces and fought other French colonies that were "loyal" to Vichy.
Now, the question is: What would be the consequences?
The problem with continuing the fight has two sides:
First side is that the French ...
tl;dr: not really.
Viable to whom?
To you and me? Sure: we know who won in the end, and we risk nothing, having been born long after the war.
To Churchill? Sure: he was committed to fighting to the end, and he would have welcomed any help.
But for a french soldier? No. The year is 1940. Germany seems unbeatable: it was starved into a defeat in WW1 by the ...