Les Cagous paid for their errors in defence by going down 2-0 to reigning champions and tournament favourites Martinique while the Toa Aito were beaten 3-1 by Mayotte.
Leading into the competition, New Caledonia coach Alain Moizan said he believed his team has the qualities to put up a good fight against some tough competition.
“We know the high level of opposition we will be facing in this competition but we are here to win,” he said.
“Despite our full calendar, we have arrived in France with the best team possible and have qualities to be proud of including our technical ability, speed and mental strength.”
Both countries must now win their next match, and are also likely to need a good result when they meet each other in the final game of Pool B, if they are to have any chance of progressing to the final.
Shortly after returning from France, Tahiti will face New Zealand’s All Whites at home and away in Stage 3 of Oceania qualifying for the 2014 FIFA World Cup while New Caledonia will face Solomon Islands in a double header of their own.
The biennial French Overseas Territories Cup runs until September 29 and involves the national teams of French overseas territories and former territories.
For highlights of the match between New Caledonia and Martinique click here
French Overseas Territories Cup
Monday 24 September
New Caledonia vs Mayotte, 4.15pm local time
Martinique vs Tahiti, 9pm local time
Wednesday 26 September
Tahiti vs New Caledonia, 5pm local time
Friday 28 September
7th/8th Play-off match, 2pm local time
5th/6th Play-off match, 4.30pm local time
Saturday 29 September
3rd/4th Play-off match (2nd Group A vs 2nd Group B), 3pm local time
Final (1st Group A vs 1st Group B), 5.30pm local time