Ross Fisher carded a 70 to join James Hepworth in a tie for fourth place at 2-under-par 140.
Heath is playing in only his fifth European Tour event of the season but the young Englishman has separated himself from the competition through two rounds at Aa St. Omer Golf Club. Heath had a strong start to the Wales Open two weeks ago but fell off pace on the weekend and ultimately tied for 44th.
'Putting the four rounds together is what I have to do now, but it's just nice to be playing good golf again,' he said. 'It would be nice to put the four rounds together but I know its going to happen eventually.'
Heath picked up a birdie at the par-3 second and added a birdie at the par-4 fifth to move to reach minus-3. He then ran off back-to-back birdies from the ninth to jump to 5 under around the turn.
The 22-year-old continued his fine play on the inward half with a birdie at the par-4 16th to secure a solid advantage heading into the weekend.
'It was just a good solid round really,' said Heath. 'I gave myself good chances and made a couple of really good up and downs when I needed to and played really well over the last few holes.'
Webster struggled out of the gate with a bogey at the first but he countered with three birdies on the front nine to make the turn at 2 under. Webster added a birdie at the 16th for a round of 68.
Edberg started on the back nine and tallied a birdie at the 10th. He gave that shot back with a bogey at the 11th but recovered with a birdie at the par-4 15th.
The 26-year-old found trouble with a quadruple-bogey at the 16th and began his damage control with a birdie at the 18th. Edberg made it two in a row with a birdie at the first and collected three birdies over his last five holes en route to a 69.
Ivo Giner, Garry Houston, Hennie Otto, Stephen Brown, Sebastien Delagrange, Gary Clark, Miguel Carballo, Rafael Gomez, David Dupart, Paul Dwyer, Adam Groom, Tom Whitehouse and Knud Storgaard share sixth place at 1-under-par 141.
The 36-hole cut fell at 3-over-par 145 with 77 players qualifying for the weekend.