Nineteen of Medvedev's twenty-one victories have been won on hard surfaces
A revitalized Medvedev secured his first title for 882 days with success over opponent Moutet in the competition title decider.
The Russian, a ex- top-ranked player, has experienced a difficult period, achieving just one win at the big events and suffering a meltdown at the US Open.
His inconsistency on the ATP Tour - and difficulties with his serve in especial - resulted in him dropping out of the top ten and ultimately separating with long-time trainer his previous coach.
Currently working with Thomas Johansson and Rohan Goetzke, Medvedev has steadily progressed in the past month - peaking in a hard-fought 7-5 4-6 6-3 triumph over opponent Moutet.
It is his maiden championship since the Italian tournament and initial on a hard surface from spring of that year.
Success also means the Russian has secured twenty-one victories at twenty-one various events.
"It's the first time I have attended a event with my both daughters at once, so to secure a title is particularly special," commented world number 14 the champion.
"This victory is in honour of my child her name, because the initial championship I achieved when my older daughter my daughter was born was for her."
Medvedev, the past champion, had been defeated in his past six title deciders, comprising in the German tournament earlier this year.
Medvedev's counter-punching strategy and frequent emotional displays on the playing surface had led commentators to doubt if his capacity to play at the top level was finished.
Yet the player has implemented adjustments in the last few weeks, attempting to come to the net and compete positively, reinforced by an better serving game.
He fought back from a deficit in the initial set against the tricky Frenchman, securing 4 of the concluding five points to gain the advantage.
The competitors traded breaks in the following set before the challenger, striving for his initial tour victory, seized the initiative to force a final set.
Moutet rescued four early-game opportunities in a competitive deciding set before Medvedev broke to fifteen to secure the win.
Suitably, Medvedev earned the win with a point at the net, with his opponent unable to control a volley after over two and a half hours.