Kyrgios argued with British umpire James Keothavong for most of the match, including a clash because Kyrgios was taking too long to change his socks. The Australian also appearaed to stop trying at one point after being warned for foul language.
Gasquet, meanwhile, at one point became enraged at his own play and destroyed his own racket.
"I'm changing my socks," Kyrgios explained to umpire James Keothavong at the changeover. "I've taken one pair off.
"I've got two on and I'm taking one pair off." After Keothavong replied to Kyrgios, the combustible Canberra man said: "I'm staying on the court. If you're going to get angry with me for that, that's another level.
"Mate, Rafa (Rafael Nadal) and stuff play 30 seconds in between points every time and all I'm doing is putting my sock back on."