Grosjean briefly got past Kobayashi on the second lap before his team mate reversed the move.
The ASM duo were nose to tail for the entire race until Kobayashi ran wide on the final lap. Grosjean tried to squeeze past but lost the rear of the car and spun.
While Kobayashi sprinted off to take the flag Grosjean was left to fend off Sebastian Buemi to hold on to second.
The clash of the team mates was the only major incident in a generally quiet race. Behind them the remaining points scorers were Yann Clairay, Franck Mailleux, James Jakes, Yelmer Buurman and Jean-Karl Vernay.
The Ultimate Motorsport duo of Esteban Guerreri and Michael Devaney were 15th and 18th in their Mygale chassis on the first appearance in the championship.
Vernay will start the second race from pole position.