Nineteen of Medvedev's 21 victories have been achieved on hard courts
A comeback Medvedev claimed his initial championship for over two years with success over opponent Moutet in the competition title decider.
The athlete, a former world number one, has experienced a torrid season, managing just one win at the Grand Slams and undergoing a difficult moment at the American major.
His varied form on the ATP Tour - and issues with his service game in especial - resulted in him exiting of the top ten and eventually parting ways with long-term mentor his previous coach.
Now training with his coach and his other coach, he has consistently progressed in the last few weeks - climaxing in a hard-fought competitive triumph over challenger Moutet.
This represents his first title since the Rome competition and maiden on a hard court after that period of that year.
The win also signifies the Russian has won 21 victories at twenty-one different competitions.
"This marks the first occasion I am participating in a event with my two daughters simultaneously, so to win a title is really nice," commented ranked player Daniil Medvedev.
"This championship is in honour of my second daughter Victoria, because the maiden victory I won when my child my daughter was born was for her."
The athlete, the past champion, had failed in his previous six finals, including in Halle previously this season.
The player's retrieving play style and regular reactions on the playing surface had caused observers to question if his skill to perform at the highest level was concluded.
However the player has implemented adjustments in the last few weeks, making an effort to come to the net and perform aggressively, supported by an enhanced serve.
The champion fought back from a break down in the opening set against the tricky Moutet, winning 4 of the last five points to gain the advantage.
The pair swapped service breaks in the following set before the Frenchman, bidding for his initial tour championship, seized the initiative to push for a final set.
He defended four initial break points in a competitive final set before Medvedev broke to fifteen to secure the win.
Appropriately, Medvedev earned the win with a rally at the net, with the Frenchman incapable to control a return after a lengthy match.