The English Challenge Tour graduate birdied the third hole of his final round to advance to 16 under par for the week with 13 holes remaining.
But Swede Jarmo Sandelin, Dutchman Robert-Jan Derksen and Dane Mark Haastrup were only one behind.
And Søren Kjeldsen, home favourite François Delamontagne and Swede Johan Edfors were right in the hunt only two shots back.
Former Ryder Cup star Sandelin carded two birdies in his first seven holes as he looks to avoid a third trip to Qualifying School in November, while Derksen pitched to five feet on the first as he signalled his intentions to launch a title charge.
Haastrup dropped a shot at the second but then chipped in at the third and birdied the next as the Qualifying School graduate, playing his first season on The European Tour, closed in on Parry.
Like Derksen, Delamontagne hit his approach to five feet at the first for birdie to boost the chances of a home winner in Paris.
There was also good news for Ryder Cup Captain Colin Montgomerie, as Padraig Harrington displayed some fantastic form ahead of next week's clash at The Celtic Manor Resort.
Having battled to make the cut on the mark, the three-time Major winner shot a third round 69 and followed that with six birdies and an eagle in the first 14 holes of his final round.
That was enough for the Irishman to rocket into the top ten, and undoubtedly boost his confidence in time to face the Americans next week.