Gaudin covered the 2.9km test in a time of 3:37 to pip compatriot Sylvain Chavanel of Omega Pharma-Quick-Step by just a second.
Lleuwe Westra of Vacansoleil was third, while Dutchman Wilco Kelderman (Blanco) was just two seconds off the fastest pace in fourth.
The 26-year-old Gaudin came into the prologue as a rank outsider for the first yellow jersey of the race, but he thrived in the streets of Houilles after successfully riding the technical sector.
Chavanel , along with Tejay van Garderen (BMC) and Westra, were all expected to shine, but Gaudin had the resilience and focus in the closing stages to leave his bigger-name rivals in his wake.
Westra looked set to seriously challenge in the final burst to the line, but he came up short with Gaudin left to celebrate what was clearly the most significant win of his career.
Thomas De Gendt (Vacansoleil), Tom Boonen (Omega Pharma-Quick-Step) and Philippe Gilbert (BMC) were all unable to stage a serious challenge, while van Garderen could only manage 59th place.
Team Sky’s Bradley Wiggins, the defending champion, is training and not involved in the race this year.
The opening stage of seven begins in Saint-Germain-en-Laye on Monday and will see the riders negotiate the 195km route to Nemours.