I think they'd both dodge each other's initial attack. You know, to weigh their opponent. If this is a random match, I'm sure they'll wanna know what they're dealing with.
After Gambit sees that Hawkeye's a pro, he won't hesitate. Hell, he can charge the very ground that Hawkeye is standing up. Gambit has too many options here.
Plus his superhuman agility will help him in the dodging. Though, in my mind, Hawkeye doesn't get the chance to attack too often with Gambit laying a barrage of attacks on him.
Good fight, tough for both, but Gambit's got too much of an arsenal, being able to charge a whole building and crap. Gambit wins after a hectic dodge-fight.