Roger-Vasselin is ranked some 184 places above Coric, but the teenager made a mockery of the apparent gulf in class by cruising to a 6-2 6-4 victory at the ATP 250 clay-court event in Umag.
Coric, who is just 17, was nerveless throughout and particularly impressed on serve, firing down eight aces and winning 70 per cent of first-serve points.
The wildcard showed his defensive qualities too, fending off all five of the break-point opportunities that Roger-Vasselin had on his way to his first ATP World Tour match win.
The world number 230 now faces either fellow Croatian wildcard Ante Pavic or Argentine qualifier Horacio Zeballos in round two.
In Monday's other first-round match, Pablo Carreno Busta had to dig deep to secure a come-from-behind victory against Paolo Lorenzi, the Spaniard eventually triumphing 4-6 6-1 7-5.
Lorenzi had two match points when serving at 5-4 in the third but he was unable to keep his nerve, as Carreno Busta reeled off four straight games to progress.
Elsewhere in the tournament, Pablo Cuevas, Andrej Martin and Marco Cecchinato joined Zeballos in qualifying for the main draw.