Nineteen of Medvedev's 21 championships have been achieved on hard surfaces
A revitalized Medvedev won his first championship for 882 days with success over opponent Moutet in the tournament final.
Medvedev, a ex- world number one, has had a challenging period, winning just one win at the big events and suffering a meltdown at the New York tournament.
The player's unpredictability on the tennis tour - and struggles with his service game in specific - caused him dropping out of the elite rankings and eventually splitting with long-time mentor Gilles Cervara.
Currently collaborating with Johansson and Goetzke, Medvedev has steadily advanced in the recent weeks - culminating in a closely contested 7-5 4-6 6-3 win over opponent Corentin Moutet.
This represents the player's initial title after the Rome competition and first on a hardcourt since that period of 2023.
Success also means Medvedev has won 21 championships at twenty-one distinct tournaments.
"It's the first time I'm at a event with my children at once, so to secure a title is especially meaningful," said world number 14 Medvedev.
"This victory is in honour of my child her name, because the maiden victory I won when my child her name was delivered was for her."
Medvedev, the 2021 US Open champion, had lost his past six finals, comprising in Halle in the past months.
Medvedev's retrieving play style and regular reactions on the playing surface had led observers to doubt if his skill to play at the highest level was concluded.
Yet the 29-year-old has altered his approach in recent weeks, striving to come to the net and compete aggressively, backed up by an improved serving game.
The champion came back from a disadvantage in the first set against the challenging Frenchman, taking 4 of the last five games to gain the advantage.
The pair exchanged breaks in the following set before the challenger, striving for his maiden professional title, seized the initiative to create a third set.
He defended 4 initial opportunities in a close deciding set before Medvedev broke to 15 to secure the win.
Fittingly, Medvedev clinched the title with a rally at the front of the court, with Moutet failing to handle a shot after two hours and 38 minutes.
