It was the second career title for Karlovic, who won the U.S. Men's Clay Court Championships in Houston, Texas in April.
The key point came when the big-serving Croat broke his eighth-seeded French foe in the 10th game of the second set to even the match at a set apiece.
He finished with 101 aces for the week and was broken just once in 64 games.
In Saturday's final one of his serves went 153 miles per hour.
"In the first set I was a little bit nervous and missed a few easy volleys," Karlovic said. "But after that, I was more relaxed and I concentrated. That was the only difference. I was playing well the whole match and throughout the week."
Clement was denied his fifth career title in his first final of the season.