France, who are ranked third in the world at this level, immediately gained composure in the game and took the lead in the 10th minute with Manssita Traore firing in for Les Bleus.
Dave Connell's team - who beat Czech Republic in their opening qualifier - started to implement their game plan as the game settled down. They moved the ball well and nullified a strong French team for long periods.
France, however, showed their class Kysha Sylla stretching their opponent in the final third as she set up multiple chance on goal that they failed to convert.
There was a chance for Aoibheann Clancy to pocket the first goal for the Girls in Green in the 20th minute but it unfortunately soared over the crossbar. An impressive attempt at goal came soon afterwards from Kerryanne Brown but she could not find the back of the net.
Connell reacted at the interval by making three substitutions, but before they had a chance to find their rhythm they conceded a penalty that Vicky Becho fired in. Trailing by two goals, it would be a long way back against such a strong opponent.
But if there is a hallmark of Connell's teams it is their fighting spirit and that was on show in the final period as they pushed France all of the way. That spark in front of goal was just missing but they gave it everything.
France wrapped up the win in the 74th minute when Jade Nassi slid a ball through the legs of goalkeeper Rugile Auskalnyte to make it 3-0 and effectively send them through to the Finals tournament in May.
Ireland will have to go again on Tuesday when they face Greece in Ostrava, Czech Republic with a kick-off time of 14:00.
France: Ines Marques, Sarah Kassi, Lou Bogaert, Thiniba Samoura, Vicky Becho (Laurina Fazer 68), Mégane Hoeltzel (Cyrille Blanc 75), Kysha Sylla, Léna Borges (Jade Nassi 68), Inés Kbida, Pauline Haugou (Louna Ribadeira 46), Manssita Traore.
Republic of Ireland: Rugile Auskalnyte, Kate Slevin (Emma Bucci 46), Shauna Brennan, Della Doherty, Therese Kinnevey, Jessie Stapleton, Aoibheann Clancy (Michelle Doonan 73), Emma Doherty (Emily Corbet 77), Erin McLaughlin, Kerryanne Brown (Becky Watkins 46), Muireann Devaney (Maria Reynolds 46).
Referee: Alina Peşu (Romania).