Advocaat was confirmed as Serbia boss on a two-year deal in July, replacing Sinisa Mihajlovic, who stepped down following the country's failure to qualify for the World Cup in Brazil.
And the Dutchman's reign got off to a respectable start in Belgrade after Aleksandar Kolarov's thunderous free-kick in the 80th minute earned the home side a draw - cancelling out Paul Pogba's first-half opener.
Speaking to reporters post-game in the Serbian capital, Advocaat was pleased with his side's performance against the Euro 2016 hosts.
"We struggled to find solutions in attack early in the game, which is normal when you play against such a team but the result is fair," Advocaat said.
"We may have been discreet in attack but we also conceded very few opportunities and that in itself is an achievement against a big team.
"The French were eventually a little dangerous on the offensive side, as were we."