Looking for his second career European Tour win -- and first since the 2002 Irish Open -- Hansen was at 7-under 206.
Englishman Simon Khan, the second-round leader, had a 70 and was alone in second place at 6-under 207.
Hansen's 66 was the round of the day at Le Golf National.
'Soren is a quality player and that 66 today was a great score,' said Khan. 'Hopefully we can go out in the final group tomorrow and have a good game and fight it out for the title.'
Playing ahead of them on Sunday will be eight-time Order of Merit champion Colin Montgomerie, who shot a 71 in the third round to end the day within three shots of the lead.
The Scotsman was joined at 4-under 209 by Germany's Martin Kaymer (69).
Montgomerie, the 2000 champion, hasn't won since the Hong Kong Open in December 2005 -- a span of 18 months. Just four of his 30 career victories have come in the last five years.
'Tomorrow I have to prove I haven't forgotten how to win,' he said.
Khan began the day with a one-shot lead on Montgomerie and Paul McGinley, but ended a shot back of Hansen after managing just three birdies and two bogeys in his round.
'I am not unhappy with that,' said Khan. 'I hit a couple of crooked shots coming in but made a great birdie at the 17th when I chipped in. I was pleased with the way I finished.'
Hansen made his only bogey Saturday at No. 2, and later closed his round with a birdie at the 18th that earned him the lead. But the highlight of his round was a 3-wood to the edge of the cup from 275 yards out at the par-five third.
He tapped in for an eagle.
'I don't think I've hit a better shot in my life,' Hansen said.
Jeev Milkha Singh shot a 67 Saturday and moved from a tie for 28th place into a share of fifth alongside Thomas Bjorn (71) and David Lynn (69) at 3-under 210.
Steven Jeppesen (68), Zane Scotland (72) and Graeme Storm (71) were another shot further back at 211.