19 of the Russian's 21 titles have been won on hardcourt
A comeback the Russian player claimed his first title for 882 days with success over opponent Moutet in the competition championship match.
The athlete, a former number one, has endured a torrid season, achieving just a single victory at the major tournaments and experiencing a meltdown at the US Open.
The player's varied form on the ATP Tour - and issues with his service game in specific - led to him exiting of the elite rankings and eventually separating with long-time coach Gilles Cervara.
Now working with Thomas Johansson and his other coach, he has steadily progressed in the past month - peaking in a closely contested three-set victory over challenger Moutet.
This represents Medvedev's first title since the Rome competition and first on a hardcourt from spring of the previous year.
Success also signifies he has won 21 victories at 21 different tournaments.
"It's the first time I have attended a tournament with my both daughters at once, so to win a trophy is really nice," said ranked player Medvedev.
"This title is in dedication of my second daughter my daughter, because the initial championship I won when my child Alisa was born was for her."
The athlete, the former major winner, had failed in his past six title deciders, including in Halle in the past months.
The player's retrieving approach and regular reactions on the tennis court had prompted commentators to wonder if his capacity to play at the highest level was finished.
However the player has implemented adjustments in the past month, attempting to come to the net and play assertively, supported by an enhanced serving game.
Medvedev fought back from a deficit in the opening set against the tricky Moutet, taking four of the concluding five exchanges to take the lead.
The competitors exchanged breaks in the following set before the challenger, striving for his initial ATP Tour title, gained dominance to push for a final set.
The opponent defended four early opportunities in a tight deciding set before the champion won the break to 15 to serve for the match.
Fittingly, Medvedev earned the title with a point at the net, with the Frenchman failing to control a return after over two and a half hours.
