Nineteen of the Russian's 21 victories have been achieved on hard courts
A comeback the Russian player claimed his first championship for nearly 30 months with a win over opponent Moutet in the tournament championship match.
The Russian, a former number one, has had a torrid period, achieving just one match at the Grand Slams and suffering a setback at the New York tournament.
His varied form on the ATP Tour - and issues with his serving in especial - led to him dropping out of the top ten and finally parting ways with long-term coach Gilles Cervara.
Currently working with his coach and his other coach, Medvedev has consistently progressed in the recent weeks - peaking in a hard-fought competitive victory over challenger Moutet.
This represents the player's maiden trophy since the Italian tournament and maiden on a hard court after that period of that year.
The win also indicates Medvedev has won 21 victories at 21 different competitions.
"This marks the first occasion I am participating in a competition with my two daughters simultaneously, so to win a trophy is especially meaningful," said tennis professional Daniil Medvedev.
"This title is in tribute of my second daughter her name, because the initial championship I achieved when my child my daughter was born was for her."
The tennis star, the former major winner, had failed in his past six title deciders, including in the German tournament earlier this year.
His retrieving approach and regular reactions on the tennis court had led some to wonder if his skill to perform at the top level was concluded.
Yet the 29-year-old has made changes in recent weeks, making an effort to approach the net and perform positively, backed up by an enhanced serving game.
Medvedev recovered from a break down in the opening set against the difficult Frenchman, taking four of the final five exchanges to take the lead.
The pair swapped breaks in the following set before Moutet, bidding for his first ATP Tour title, seized the initiative to force a final set.
He rescued four early chances in a close final set before the Russian broke to fifteen to close out the victory.
Suitably, Medvedev clinched victory with a point at the front of the court, with the Frenchman failing to control a shot after two hours and 38 minutes.