Their task was made easier by the fist-half dismissal of Wilson Palacios and Deschamps revealed that he was pleased at the display from his players.
"This is a very good start," he told TF1. "We've had good times during our preparation, but this is competition. Winning today is a very good start.
"We will enjoy this victory... 3-0 win in the World Cup, because it's never easy. We have been patient. We had our chance and hit the bar twice in the first period.
"We did well. Pleasure is total in football when there is victory. Congratulations to the players."
France will take on Switzerland in their second Group E match on Friday.