Garry Houston was three shots back at 5-under-par 137. Peter Hanson, Paul Broadhurst, Sebastien Branger and Michael Kirk followed at 4-under-par 138.
Rumford, who enjoyed a bogey-free round on Thursday at Aa Saint Omer Golf Club, found trouble early in his second round. He played the back side first and dropped two shots with a pair of bogeys over his first three holes.
The 25-year-old countered with a birdie at the par-4 18th and hit his approach to 12 feet at the par-4 first to make it two in a row and return to 7-under.
Rumford then tallied a two-putt birdie at the par-5 ninth, his last, to keep his grip around the lead heading into the weekend.
'It was a different day,' said Rumford, whose best finish on the European Tour this season is a tie for 22nd at the Johnnie Walker Classic. 'The putter wasn't hot today. The greens were tricky and I had a lot of good putts which didn't drop. I played well and could have scored better but overall I'm quite pleased.'
The Australian, who is working towards regaining his European Tour card, has put himself in a good position at this former Challenge Tour event.
Salto struggled early with a bogey at the par-3 fourth but recovered with a remarkable play at the par-4 eighth. Salto's second shot left him 80 feet from the hole but the Spaniard ran home the putt for a birdie.
He added a birdie at the 10th and closed with three birdies over his last five holes to finish one shot off the lead with a round of 67.
'I've been playing well and finally put a score together,' said Salto, who stands at 7-under-par 135. 'I put a lot of pressure on myself last year and couldn't get a result. This year I am trying to do things a little different and enjoy the courses a little more. I am a lot happier and hope to carry on like this for the weekend.'
Stuart Little shot a 4-under 68 to finish five shots off the lead in a tie for eighth. Little was joined by Mattias Eliasson, Ben Mason, Michele Reale, Martin Erlandsson and Cesar Monasterio at 3-under-par 139.
The 36-hole cut fell at 3-over-par 145 with 78 players qualifying for the weekend, including last year's champion Nicolas Vanhootegem.