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The 42-year-old, who will have an operation in Zurich next week to deal with the long-standing problem, birdied his final hole for a five under par 66 on the course outside Versailles that will stage the 2018 Ryder Cup.
He had seven birdies and only two bogeys on a day when many players in a top class European Tour field struggled over the demanding four-holes closing stretch.
Hansen's only bogeys came at the first and eighth - the latter after leaving his chip ten feet short of the hole.
Those dropped shots sandwiched birdies from eight feet at the fifth and 30 feet on the sixth, after the three-time European Tour winner had gone out in 31.
"I'm telling you, it's a great venue for The Ryder Cup," Hansen enthused.
"The course is set up perfect for it. The spectators get such a good view and it's such a great finish to the round - I think it's going to be a great venue.
"It is a tough course - the greens are pretty firm and it's tight out there. There's hardly any wind, and you see the scores aren't that great.
"I played actually really solid from tee to green - I think I only missed two or three greens. I putted quite well, so just sort of all came together.
"At some stage it seemed a bit easy, but this course gets your attention and next thing you know, you're making bogeys."
On the topic of his painful hand Hansen, who won the last of his three European Tour titles more than four years ago in South Africa, added: "I'm having my operation on Tuesday, so I'm looking forward to get that out of the way and hopefully be ready for the end of the season.
"It's not far away, so I'm looking forward to get that done.
"I've had it for years and years and years - they are going in three different places and they are going to remove a cyst I have here and clean this up and hopefully there's a 50/50 chance it's going to be okay."
Hopes of a first home win since Thomas Levet in 2011 were boosted by emerging star Romain Wattel, who finished the day second on four under 67, one shot ahead of a large group containing 2009 winner Martin Kaymer of Germany.
The 22-year-old Wattel was able to limit the damage done by bogeys at the 15th and 16th with six birdies - a couple of them the result of monster putts.
"You are in front of the French crowds, so you want to be good, you want to play great golf and so there is pressure on me," said Wattel, who has already impressed this season with a third-place finish in Austria and fourth in Korea.
"I'm trying to play my best and just focus on the shot I have to play - that's the only thing I can do."
Ryder Cup stars Luke Donald and Graeme McDowell shot respectively 71 and 69 to stay well in contention.
Collated first round scores in the French Open at Le Golf National outside Versailles on:
(GBR & IRL unless stated, par 71)
66 - Anders Hansen (DEN)
67 - Romain Wattel (FRA)
68 - Matthew Nixon, Estanislao Goya (ARG), Martin Kaymer (GER), Victor Dubuisson (FRA), Felipe Aguilar (CHI), Stephen Gallacher, Thomas Bjorn (DEN), Fabrizio Zanotti (PAR), Richard Sterne (RSA)
69 - Soren Kjeldsen (DEN), Richie Ramsay, Graeme McDowell, David Howell, James Morrison, Scott Jamieson, Marc Warren, Miguel Angel Jimenez (ESP), Richard Green (AUS), Gregory Bourdy (FRA), Michael Hoey, Alexander Levy (FRA)
70 - Alan Dunbar, Damien McGrane, Ross Fisher, Garth Mulroy (RSA), Jaco Van Zyl (RSA), Simon Dyson, Graeme Storm, Alexander Noren (SWE), Bernd Wiesberger (AUT), Rafael Cabrera Bello (ESP), Michael Campbell (NZL), Mark Tullo (CHI), Matt Kuchar (USA), Raphael Jacquelin (FRA), David Drysdale, Jamie Donaldson, Chris Lloyd, Thomas Pieters (BEL)
71 - Mikael Lundberg (SWE), Francesco Molinari (ITA), Thomas Aiken (RSA), Joost Luiten (NED), Morten Orum Madsen (DEN), Jose Manuel Lara (ESP), Thongchai Jaidee (THA), Robert Rock, Alessandro Tadini (ITA), Alejandro Canizares (ESP), Pontus Widegren (SWE), Hennie Otto (RSA), Gareth Maybin, Matthew Baldwin, Andrew Dodt (AUS), Matthew Southgate, Lee Slattery, Simon Khan, Seve Benson, Luke Donald, Mark Foster, Christopher Doak
