Celene/Briala, sometimes making three of them work together (though IMO that's a ticking time-bomb, more than C/B is, at any rate) and sometimes Celene alone.
Gaspard? Never. Not in my "decent" plathroughs at least.
Really, I see no reason to put him on the throne. People already have "a leader for difficult times" - which is Inquisitor, who just hand-picks who rules Orlais anyhow and has at least 3-4 years (1-2 years prior to Cory defeat and 2 after) to order people around and get the gist of the hardest work done to stabilize the region. Orlais needs calm heads and time to recover, not warmongerers with simplistic dreams to expand Empire via conquest.
As for Gaspard and Briala? ...Nope. Briala is charismatic and determined, but she's overzealous in her mission - if she's going to co-rule, she needs Celene to temper her down (while Celene needs her to be bolder with reforms). Besides, considering that we find out that she loses eluvian network and likely a lot of her spies to Solas, she's only really useful as inspiration for Celene to do better for elves (assuming optimistically that they wont' have a falling out) - because I don't predict that she'd survive long trying to control Gaspard, especially if more Orlais elves leave the country for whatever mysterious reasons draw them to some remote wilderness....