Djokovic clinched his sixth singles win in six outings this year in the tournament as Serbia, backed by a noisy, passionate crowd at the Belgrade Arena, kept their dream of a first Davis Cup title on track.
Gael Monfils had earlier handed nine-time champions France a 1-0 lead with a 6-1, 7-6 (7/4), 6-0 victory over Janko Tipsarevic.
Djokovic was always in control against world number 42 Simon, who had been handed the second French singles berth in the absence of injured Jo-Wilfried Tsonga, and wrapped up the rubber after 2hr 18min on a fourth match point.
Serbia's top player, who could be called into doubles action on Saturday, praised the Belgrade crowd.
"Definitely it's an advantage for the home team playing in front of their people. To be able to have this support is really relevant," said Djokovic.
"This competition depends on crowd support. That's why this competition is very unpredictable and unique, especially at the later stages where you play top players. The crowd gives you extra if you're tired."
Monfils, the French number one who is ranked 12th in the world, displayed none of the nerves he feared would emerge in the opening rubber of France's campaign for a 10th crown.
In spite of a cold, the 24-year-old Parisian instead displayed composure in front of the largely partisan crowd as he sailed through the first set, handled a more determined charge from Tipsarevic in the second and dominated the third as his opponent crumbled.
Monfils admitted Tipsarevic's shaky start, which included two double faults, helped settle his own nerves: "I got into the match straight away and that helped settle me," he said.
"I'm really happy with the result. Janko started off with two double faults, and straight away I saw that he was tense. That helped me to relax a little."
Tipsarevic, who was Serbia's hero in the semi-final defeat of the Czech Republic, was on occasion subject to jeers and whistles from some sections of the crowd in the third set.
"I feel the crowd was fair. They were whistling sometimes in between serves," said Tipsarevic.
"This is the Davis Cup final. It wasn't anything drastic or dramatic. I was feeling the pressure. But then again I was the underdog. Even though we were playing at home, everybody was expecting Gael to win, which eventually happened."
Michael Llodra and Arnaud Clement will represent France in Saturday's doubles encounter when they are due to meet Nenad Zimonjic and Viktor Troicki while the reverse singles will be on Sunday.
However, Troicki could make way for Djokovic.