Nineteen of the Russian's 21 titles have been earned on hard courts
A resurgent Medvedev won his maiden trophy for 882 days with a win over opponent Moutet in the tournament final.
The Russian, a ex- world number one, has had a difficult season, managing just one win at the big events and suffering a setback at the American major.
His varied form on the professional circuit - and struggles with his serving in particular - led to him falling of the elite rankings and eventually splitting with former mentor his previous coach.
Presently working with Thomas Johansson and Goetzke, the tennis star has steadily improved in the past month - peaking in a hard-fought competitive triumph over challenger Moutet.
This represents the player's initial championship since the Rome competition and maiden on a hard surface after March of the previous year.
The win also signifies he has achieved 21 championships at twenty-one different events.
"It's the first time I am participating in a tournament with my children together, so to secure a title is particularly special," stated world number 14 the champion.
"This title is in tribute of my younger daughter my daughter, because the first title I achieved when my older daughter Alisa was born was for her."
The athlete, the past champion, had lost his previous six finals, comprising in Halle earlier this year.
The player's retrieving strategy and recurring outbursts on the tennis court had caused commentators to question if his skill to compete at the elite level was over.
Yet the athlete has altered his approach in recent weeks, striving to advance forward and perform positively, backed up by an improved serve.
Medvedev came back from a disadvantage in the initial set against the tricky opponent, winning 4 of the final five exchanges to take the lead.
Both players swapped breaks in the middle set before the Frenchman, attempting for his initial ATP Tour championship, seized the initiative to push for a final set.
Moutet rescued four early-game break points in a close deciding set before the Russian won the break to fifteen to serve for the match.
Suitably, he clinched the win with a shot at the net, with Moutet failing to manage a shot after over two and a half hours.
