The 29 year old, who returned to The European Tour via November's Qualifying School, shot a third round 68 to reach seven under par at Aa Saint Omer Golf Club.
That put the former Walker Cup star one clear of Challenge Tour leader Robert Dinwiddie and home favourite Raphaël Jacquelin.
Two-time European Tour winner Jacquelin, the highest-ranked player in the field, carded a best of the day 66 to move into contention, while overnight leader Dinwiddie stayed in the hunt with a level par 71.
Elson began the day with a bogey, but hit straight back at the par three second and consecutive birdies at the sixth and seventh took him to the turn in 34.
He began the back nine with three birdies in four holes, but late dropped shots at the 15th and 16th kept the door ajar for the chasing pack.
“Around the turn I made some really good birdies.,” said Elson. “At ten I made a really good read, nice three there. Played the 12th great too and at the 13th holed a relative monster for this course.
“There’s such a long way to go and in these conditions anything could happen. Just a case of staying grounded and doing what I’ve been doing these last few days.
“There’s just so many difficult holes out there, it’s a case of making as many pars as you can and if you can make any birdies then that’s a bonus.”
Dinwiddie lost his European Tour card last year, but has set about regaining his playing privileges with victory at the Kenya Open.
The 27 year old knows that victory on Sunday would secure his return but after a stunning 65 in the second round he could only mix four birdies with four bogeys in his third round.
“I’m not out of it – that’s the positive to take,” said Dinwiddie. “I holed some good putts. I feel kind of lucky to be where I am. I hit the ball alright off the tee but hit some horrible iron shots.
“I’ve still got a shot at it tomorrow – that’s the main thing. But I’m going to need to hit the ball better to have a chance.”
Jacquelin, the World Number 154, flew out of the blocks with a front nine 32 which included a second eagle of the week at the par five seventh for last year’s Barclays Scottish Open runner-up.
“I holed many putts today – and that’s made a big difference to the score,” said Jacquelin.
“I’ll try and keep the same feeling for tomorrow and play as good as I did today and I should be alright.”
Dane Mark F Haastrup looks set for another good finish after coming third at last week’s Estoril Open de Portugal – he sits in a share of fourth with Austrian Martin Wiegele on four under.