Nineteen of the Russian's twenty-one victories have been earned on hard courts
A comeback Medvedev secured his first trophy for 882 days with success over Frenchman Moutet in the tournament final.
Medvedev, a former world number one, has had a difficult period, managing just one match at the Grand Slams and suffering a setback at the US Open.
The player's inconsistency on the professional circuit - and struggles with his serve in particular - caused him exiting of the world's top 10 and eventually separating with long-term coach his previous coach.
Currently collaborating with Thomas Johansson and his other coach, the tennis star has consistently advanced in the last few weeks - peaking in a closely contested 7-5 4-6 6-3 triumph over opponent Moutet.
This represents Medvedev's first trophy since the 2023 Rome Masters and initial on a hardcourt after March of 2023.
The win also indicates he has achieved twenty-one titles at 21 various competitions.
"This marks the first occasion I have attended a event with my children together, so to secure a title is particularly special," commented world number 14 Daniil Medvedev.
"This title is in honour of my second daughter my daughter, because the first title I achieved when my child Alisa was born was for her."
Medvedev, the 2021 US Open champion, had failed in his previous six championship matches, comprising in Halle previously this season.
His retrieving play style and recurring emotional displays on the playing surface had led some to question if his skill to perform at the highest level was over.
Yet the 29-year-old has implemented adjustments in recent weeks, making an effort to advance forward and compete assertively, reinforced by an enhanced serve.
He recovered from a disadvantage in the first set against the challenging opponent, winning four of the last five points to go ahead.
The pair traded service breaks in the middle set before the Frenchman, attempting for his maiden tour title, gained dominance to push for a final set.
He saved four early-game opportunities in a tight final set before Medvedev won the break to that score to serve for the match.
Appropriately, the winner clinched the title with a rally at the net, with his opponent unable to manage a shot after over two and a half hours.
