Conor McGregor was rubbin' elbows with ROYALTY on the French Riviera on Monday ... racing water bikes with Princess Charlene of Monaco and the pics are awesome.

The two got in a workout while Conor and his family are in the area on vacation. Afterward, their families -- including Prince Albert -- hung out together on shore.

"A Great day racing the water bikes with Princess Charlene of Monaco," Conor said.

"A phenomenal athlete and Olympian, we are teaming up for a 180km voyage in September to raise awareness in water safety. I cannot wait!"

It's true ... Princess Charlene is one hell of an athlete herself -- a former Olympic and World Champion swimmer!

In fact, she competed for South Africa in the 2000 Olympic Games in the 4x100 relay, fishing behind Team USA (led by Olympic legend Amy Van Dyken).

She retired from competitive swimming in 2007 -- and now focuses on various philanthropic efforts including water safety and the Special Olympics.

McGregor was clearly impressed with the water bike workout -- saying he will now incorporate the exercise into his McGregor F.A.S.T. training program.

"Thank you for the great day for my family Your Highness," McGregor added ... "In aid of the Princess Charlene of Monaco foundation."