Les Bleus, back in the mix since Galthie took over last year, scored a try through Charles Ollivon on their first incursion and defended stoutly in a tense finale to snatch their second win in two games in this year's championship.
France, who host the 2023 World Cup, top the standings with nine points, ahead of Wales on goal difference with England in third place three points adrift.
"We were prepared to win the game, we won the game. It was our objective. That's it," Galthie, who has led France to nine victories in 11 games, told a news conference.
"We have a lot of ambition, for all our games. We were ready to face the Irish. It's interesting to tick the boxes. Each game is not a goal in itself, we have bigger goals. I think the team will continue to improve."
France suffered in the rucks and struggled in the lineouts in the first half but never panicked and punished Ireland on their first foray, a series of offloads leading to a clinical try by Ollivon before Damian Penaud added another after the break.
"When we have an opportunity, we convert it, although we could have done better on that front," said centre Gael Fickou, a veteran with 60 caps in a relatively inexperienced team.
Les Bleus performed under the pressure of Ireland's high kicks, with fullback Brice Dulin providing the team with a safe pair of hands.
"This win is the result of all the work we've put in in the last 18 months. We're not there yet, far from it," said Dulin.