Les Bleus looked like World Cup contenders as they raced into a 13-0 lead with some outstanding rugby capped by Vincent Clerc's try.
But they fell away in the second half and Ireland took advantage by staging a fightback inspired by Ronan O'Gara that ultimately fell short.
"I'd hate to go back into the past and say that I'm glad we had a really good second half," said Kidney.
"That's the sort of thing we would have said in the past. We lost the game and that's what we need to look at it.
"In the first half we did a bit of damage to ourselves because we didn't hang on to the ball too well.
"At the start France played well and we didn't play like we're capable of.
"When you put those together you'll end up doing a lot of defence.
"Our defence has had a lot of practice over the last couple of weeks.
"We must look at doing more of what we did in the second half, but one half doesn't count - you must do that for 80 minutes."
Full-back Rob Kearney, who returned from a serious knee injury only last weekend, limped off with a groin problem.
"Rob pulled up with a tight groin. I'd hope it's not serious," said Kidney.
France coach Marc Lievremont was satisfied after his side won the first of their two warm-up internationals for the World Cup.
Lievremont was delighted with the opening quarter when the French looked like a side who could challenge the world's best in New Zealand, and refused to be dispirited by their subsequent collapse.
"I'm happy because our first goal was to win our last match in France before the World Cup. Now we must build on this," he said.
"The first third of the match was great. Maybe that had a strong impact on our game, perhaps the players were overwhelmed.
"The players became tired, but we're very happy with the intensity we showed in the first half.
"We know what worked on the pitch and also what didn't work so well. We know what we must address for the next game."
Centre Maxime Mermoz suffered knee ligament damage but Lievremont believes the injury is minor.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
