Hometown favorite Jean-Francois Lucquin stands alone in third place at 3-under-par 68, with Marc Farry, Massimo Florioli, Mikael Lundberg, Stephen Browne and Marc Cayeux one stroke further back at minus-2.
This event has a split field of Challenge Tour and regular European Tour players as many of the world's best are competing at the U.S. Open this week.
Sullivan opened on the back nine of the Val Course at Aa Saint Omer Golf Club and parred his first two holes. He then wrapped birdies at 12 and 14 around a bogey at the 13th.
Sullivan, who turns 28 years old next Tuesday, dropped in birdie at the par-3 17th to make the turn at minus-2. However, he stumbled to a double bogey at the par-4 third.
The Challenge Tour player then caught fire down the stretch. He drained a 3-foot birdie at No. 6 and came right back with a two-putt birdie at the par-5 seventh. He made it three in a row when he birdied the par-4 eighth.
Sullivan knocked his second shot to the par-5 ninth on the green and rolled home the eagle to grab the overnight lead.
'I finished very well today,' said Sullivan. 'I just hope that I can keep it going for the rest of the week. This is only my second European Tour event, after playing in the Madeira Island Open earlier in the year so I am just going to see how I get on and hopefully maintain that kind of form.'
Barham dropped a shot at the third, as he played the first six holes at 1-over par. He picked up birdies at the seventh and ninth to make the turn at minus-1.
The 28-year-old Barham dropped his second shot to par at the 10th to slip back to even-par. He came right back with a birdie at the next and birdied the 14th to get to minus-2.
Barham closed with back-to-back birdies from the 17th to move into second place after the opening round.
Simon Dyson and Alessandro Tadini are among a group of players tied for 10th at 1-under-par 70. They are joined there by David J. Geall, Greig Hutcheon, Jamie Little, Juan Abbate, Gregory Bourdy, Gustavo Rojas, Alvaro Salto, Carl Suneson and Murray Urquhart.
Andrew Raitt and Jorge Berendt lead a group of 18 players at even-par 71.