Nineteen of Medvedev's twenty-one titles have been achieved on hard surfaces
A comeback the Russian player secured his maiden championship for over two years with a win over Frenchman Moutet in the tournament title decider.
The Russian, a former world number one, has experienced a torrid period, achieving just one win at the Grand Slams and suffering a meltdown at the American major.
Medvedev's varied form on the ATP Tour - and struggles with his service game in especial - led to him exiting of the world's top 10 and eventually splitting with long-term coach Gilles Cervara.
Presently working with his coach and Goetzke, the tennis star has gradually advanced in the recent weeks - climaxing in a closely contested three-set victory over opponent Corentin Moutet.
This represents his first title after the 2023 Rome Masters and initial on a hard court after that period of that year.
Success also indicates he has secured 21 victories at 21 distinct events.
"This marks the first occasion I'm at a competition with my both daughters together, so to win a trophy is particularly special," commented ranked player the champion.
"This title is in honour of my child my daughter, because the maiden victory I won when my first daughter my daughter was born was for her."
The tennis star, the former major winner, had lost his previous six championship matches, comprising in the German tournament earlier this year.
Medvedev's defensive approach and regular reactions on the tennis court had prompted commentators to wonder if his skill to compete at the elite level was finished.
However the athlete has implemented adjustments in the last few weeks, striving to advance forward and perform assertively, supported by an improved serving game.
He fought back from a disadvantage in the opening set against the difficult Frenchman, winning 4 of the concluding five exchanges to take the lead.
Both players swapped breaks in the second set before the Frenchman, attempting for his initial ATP Tour victory, took control to create a decider.
He saved four early chances in a competitive third set before the champion broke to that score to serve for the match.
Fittingly, he earned the win with a shot at the front of the court, with the Frenchman failing to manage a shot after a lengthy match.