The national team has been involved in a number of off-field controversies at tournaments in recent years, including the infamous disagreements between players and former coach Raymond Domenech at the World Cup in 2010.
Further squad tensions saw France eliminated from Euro 2012 at the quarter-final stage when Laurent Blanc's side had looked on course to go deeper into the tournament.
Deschamps took over following that tame exit to Spain and, after a last-eight defeat to eventual World Cup winners Germany in Brazil earlier this year, France are unbeaten so far in their friendlies leading up to the Euros in two years' time.
The former France international feels his side have captured the imagination of their public once again.
"The fans really fell out of love with the team after what happened in South Africa in 2010," he told FIFA.com.
"The players' performances on the pitch have caught the imagination of the French fans again. It goes without saying that it’s nicer for the players to be loved than hated.
"It's up to us, in every game we play from now on, to make sure the fans turn up in numbers, cheer us on and get behind this France team."
France continue their preparations for the Euros this month with friendlies against Albania and Sweden, having beaten Portugal and Armenia in recent weeks.
Deschamps is not concerned by the lack of competitive matches for his side and insists his relatively young team are making progress.
"They're friendly matches and we won't be playing anything other than friendlies in the build-up to the Euros, though we've obviously got some high-profile matches coming up," he added.
"We've played Spain and we're going to play Italy, England, the Netherlands and Germany. Though we're already in the finals, we want to finish top of our group, even if it doesn’t really count.
"Every team makes progress, mine included. The players are getting to know each other better and as I’ve already said, I've got a lot of young players. You can't pick up experience from one day to the next.
"You need time and there are maybe some other young players who can come in for the next competition."
