Nineteen of the Russian's 21 victories have been earned on hard courts
A revitalized Medvedev secured his initial title for over two years with a win over opponent Moutet in the competition championship match.
The Russian, a ex- world number one, has experienced a difficult period, winning just one match at the Grand Slams and suffering a difficult moment at the US Open.
His varied form on the tennis tour - and struggles with his serve in specific - led to him exiting of the top ten and finally separating with long-term mentor his previous coach.
Currently collaborating with Johansson and Goetzke, the tennis star has consistently advanced in the last few weeks - culminating in a hard-fought three-set triumph over challenger Moutet.
This marks the player's initial trophy since the 2023 Rome Masters and first on a hard surface after spring of that year.
Victory also signifies he has won 21 victories at twenty-one different competitions.
"For the first time I have attended a competition with my both daughters together, so to win a title is particularly special," said ranked player Medvedev.
"This victory is in tribute of my child Victoria, because the maiden victory I won when my older daughter her name was born was for her."
Medvedev, the past champion, had lost his last six championship matches, including in the German tournament earlier this year.
Medvedev's retrieving strategy and recurring outbursts on court had caused observers to question if his skill to compete at the highest level was finished.
But the athlete has implemented adjustments in the last few weeks, striving to approach the net and compete aggressively, backed up by an enhanced serve.
He recovered from a deficit in the first set against the challenging opponent, taking four of the concluding five points to gain the advantage.
The pair exchanged break points in the middle set before the Frenchman, bidding for his maiden professional title, took control to create a decider.
He saved four initial opportunities in a tight final set before the champion broke to that score to secure the win.
Fittingly, Medvedev earned the title with a shot at the front of the court, with the Frenchman unable to handle a return after two hours and 38 minutes.
