Martial, 22, has found form for United, scoring five goals in his past six games to earn a recall to the France squad.
Deschamps hopes the former Monaco star is maturing, challenging the forward to maintain his recent form.
"Anthony has been with the national team for a while now. He's experienced both good and bad times, which is also the case for his club," he told a news conference on Thursday.
"What he's currently achieving with Manchester United is closer to what he's able to do regularly. I'm talking about commitment and efficiency in front of goal.
"He's a young player and I hope he is becoming more mature. He has proved that on the pitch by how important he's been for Manchester United for a few weeks already.
"It's obvious by Jose Mourinho's choice [to start Martial] and what he's doing on the pitch."
Martial has six goals in 13 games in all competitions this season and could add to his 18 France appearances when Deschamps' men meet Netherlands and Uruguay later this month.
The Manchester United winger isn't the only young player Deschamps is both impressed with and challenging to improve as the manager once again heaped praise on the "extraordinary" Kylian Mbappe ahead of the upcoming matches.