Nineteen of Medvedev's 21 championships have been won on hardcourt
A resurgent the Russian player secured his first trophy for over two years with success over opponent Moutet in the tournament title decider.
Medvedev, a ex- world number one, has endured a torrid period, achieving just a single victory at the Grand Slams and experiencing a difficult moment at the US Open.
His varied form on the tennis tour - and issues with his service game in particular - caused him falling of the top ten and finally parting ways with long-term trainer his previous coach.
Currently training with Thomas Johansson and his other coach, he has gradually advanced in the last few weeks - peaking in a tightly fought competitive victory over Frenchman Moutet.
This marks Medvedev's initial title following the Rome competition and maiden on a hard surface from March of the previous year.
The win also signifies he has won 21 victories at 21 different events.
"It's the first time I am participating in a tournament with my children simultaneously, so to win a title is especially meaningful," said world number 14 Medvedev.
"This victory is in honour of my child Victoria, because the initial championship I achieved when my first daughter my daughter was born was for her."
The athlete, the past champion, had been defeated in his past six title deciders, featuring in Halle earlier this year.
His defensive play style and regular emotional displays on the tennis court had led some to question if his capacity to play at the elite level was finished.
But the player has altered his approach in recent weeks, striving to come to the net and compete positively, backed up by an improved serving game.
He came back from a deficit in the opening set against the challenging opponent, securing 4 of the final five exchanges to gain the advantage.
Both players traded breaks in the middle set before the Frenchman, striving for his initial tour championship, gained dominance to push for a third set.
Moutet rescued four initial break points in a tight deciding set before Medvedev secured a break to that score to secure the win.
Fittingly, he clinched the title with a shot at the net, with Moutet failing to handle a shot after two hours and 38 minutes.
