Démare was the winner and first leader of Paris-Nice in 2017 and held the race lead for several days and this time he repeated the feat but in a finale perhaps not best suited to his talents.
The Groupama-FDJ leader battled his way to the win with Gorka Izagirre (Bahrain-Merida) Christophe Laporte (Cofidis) and Tim Wellens (Lotto-Soudal).
The quartet finished together after a punchy and technical closing five kilometres which finished up a gradient on a narrow cobbled section in the town of Meudon on the outskirts of Paris.
Thanks to bonus seconds awarded to the winner Demare leads Izagirre by four seconds in the overall standings going into the second of eight stages.
"This is the first photo-finish in my career, it had never happened before so it was a real explosion of joy when I was told," Démare said.
"I was convinced I was second. When I threw my bike towards the line, it was more out of despair. I was certain I had lost it. In the end you are not totally lucid.
"It's also my first win on top of a bump like this. It hurt a lot but I kept solid in my head in front of my fan club and my family.
"I had checked it yesterday by car and it looked harder than it was on the bike. With a kilometre to go, Alexis Vullermoz was still in the front and I was dead but I decided to go early, not thinking I could go all the way.
"I'm so happy because it's my first victory of the year, the first for our new sponsor, there was a lot of pressure."
Brenton Jones is originally from Jindivick in Victoria and currently riding for UCI Professional Continental team Delko–Marseille Provence KTM based in France.
Jurgen Roelandts (BMC), Pierre-Luc Perichon (Fortuneo) and Pierre Rolland (Education First-Drapac) got the rainy race started with a break which topped out at 3min 35sec before the peloton decided that was enough.
As the gap narrowed, Roelandts took the two intermediate sprints and Perichon the mountain points before their efforts ending with 14km to go.
Mitchelton-Scott, Astana and Lotto-Soudal took turns in the final 10 km before Alexis Vuillermoz surged. The AG2R rider seemed to have the stage in hand but he faltered in the long cobbled finale and was overtaken by the front of the bunch, led by Izagirre, who battled it out with Demare, Laporte and Wellens.
Démare threw his bike to the line in despair and the outcome was so close that the four top finishers had to wait for the photo-finish to discover who had actually won.
American Tejay Van Garderen (BMC) pulled out after a nasty fall on the rain-slick 135km route.
Stage 2 runs 187.5km from Orsonville to Vierzon and is set for another sprint finish.
Watch stage 2 live from 1:20am AEDT Tuesday 6 March streaming here and broadcast on SBS.