Declan Sheridan's side took the lead early on when quick thinking from Jodie Dillon saw him take the ball away from goalkeeper Yannick Germannaud and slot into an empty net.
The visitors left it late to hit back when Antoine Goulard fired in on 81 minutes to level matters and that is how it stayed until the final whistle sounded - providing a relatively fair outcome from a competitive encounter.
Preparations for this tournament were disrupted slightly by the withdrawal of both Greece and Azerbaijan, which forced a change of schedule to pit the Irish outfit against their French counterparts over two legs.
The winner of this tie will then progress to the European final against the top team from the other group, which contains Germany, Netherlands, Poland and Lithuania, while they will also secure a place at the 2017 World Military Games in Oman.
"I felt that we had the better of the chances overall, but we will take the draw. It gives us a decent chance of qualifying and we can take a lot of positives from this game," said Sheridan.
"The French side were technically excellent and highly motivated. We are well used to playing against them and the last three times we have played them competitively we have come out on the wrong side, so a draw was pleasing from that point of view.
"Regardless of the result though I couldn't be prouder of the lads. They have been outstanding in their commitment to these games and now we are one step closer to qualifying. It's winner takes all on Wednesday."
Sheridan's team will meet the French again on Wednesday at 11:00 at Eamonn Deacy Park, where victory would seal their place in the European final and at the World Military Games.
Irish Defence Forces: K Deegan; Fox, Long, Delaney, Kenny, Dempsey, Friel, Wall, Dillon (J Deegan 62), Gethins (Duffy 82), Gannon (Walsh 71).
French Armed Forces: Germannaud; Trinite, Rossignol, Kamba, Goulard, Dupuis (Jougounoux 59), Abriel, Laplace Palette, Asbabou (Pannier 77), Coulomb, Oggad (Moatti 71).