Lisa Vittozzi anchored host nation Italy to the silver medal and Germany picked up the bronze.
The French finished in a time of one hour 4:15.5, with Italy 25.8 seconds further back and Germany over a minute behind the winner, but the day belonged to Simon as she shut the door on the rest of the field.
Simon’s French team, consisting of Lou Jeanmonnot, Eric Perrot and Quentin Fillon Maillet, had their fair share of misses on the shooting range, but she displayed nerves of steel on the anchor leg, rattling off a flawless 10 shots on her two visits to the range to save the day.
Simon hails 'great team effort'
"I did a great relay, but it was a great team effort. I really enjoyed myself. I'm very, very happy with how I performed in this race," an elated Simon told French TV.
"It's magical. I don't think I realise it yet, these are such huge events," teammate Perrot said after securing gold in his maiden Olympic race.
With the crowd primarily made up of fanatical fans from Italy, Germany and France, they all got what they came for as Vittozzi, who is renowned for being quick on the trigger, held her nerve to emerge into the last lap in second place.
Germany shot brilliantly until the final visit to the range where the vastly experienced Franziska Preuss had some uncharacteristic misses, but she recovered to hold off a late Norwegian challenge to take the bronze.
Disappointment for Norway and Sweden
While the drama happened on the shooting range, the race was won out on the course as the French four made the most of their fast skis to deliver a team performance of enormous power, regularly eclipsing the best lap times of their rivals.
There was disappointment for Norway, who made the running early on but fell away towards the end, and Sweden's challenge fell apart at the first shoot as lead-off man Sebastian Samuelsson struggled to hit the target, digging his team into a hole they could not get out of.
There was joy for local Italian hero Dorothea Wierer, who has taken a bronze medal at each of the last three Olympics, and on Sunday she finally went one better, securing a silver medal that brought roars of approval from the grandstand.