Conor McGregor and Fiancee, Do We Look Worried?!

United front from Conor McGregor and fiancee Dee Devlin in the wake of some serious criminal allegations in Corsica ... posing together in a waiting room in Italy.

Neither Conor nor Dee look bothered in the pics -- they still seem to be in vacation mode, despite the police investigation over an alleged attempted sexual assault earlier this month.

Worth noting ... the sign above the couple says (in Italian) they're in a waiting room at a doctor's office (an ear specialist). Hopefully, everyone's okay.

The McGregor family has been busy over the past few weeks -- French officials say the UFC star was detained and questioned over the alleged Sept. 6 incident.

Just the other day, Conor declared in a social media message that the allegations against him are "bullish*t" and that he refuses to pay a dime "to anyone coming at me with vicious lies."

Conor and his family -- including his children and his parents -- have been sailing around the Mediterranean on his yacht.

He was supposed to participate in a water bike race with the Princess of Monaco this past weekend but backed out due to his legal issues.