Cool! To bad I don't speak French.
But I do, so let me help here.
0:11- Pilot; C'est parti! (It's a go!)
0:11- Léa; Pi! (Yeah! in "baby-talk)
0:53- Pilot; On y vas doucement... (We go gently...)
0:55- Pilot; On accélère... (We pick-up speed...)
0:58- Pilot; On tire... (We pull...)
1:10- Pilot; Là on vas y aller un peu fort. (Now, we're gonna go a bit stronger.)
1:11- Léa; Vas-y! Allez à l'envers! (Let's go! Go upside-down!)
1:27- Léa; C'est drôle! (It's funny!)
1:27- Pilot; Oui? (Yeah?)
1:29- Léa; C'est trop drôle! (It's too funny!)
1:37- Pilot; OK (after talking briefly with control)
1:38- Pilot; Là on a été sur le côté. (We just went on the side.)
1:39- Léa; Papa, encore la tète à-l'envers! (Daddy, again upside-down!)
1:41- Pilot; Oui? Attends Léa. Là, on a été sur le côté. On en refait un? (Yeah? Wait Léa. We went on the side. Do we do it again?)
1:45- Léa; Je veux encore la tête à-l'envers! (I want head upside-down again!)
1:47- Pilot; C'est parti! (Here we go!)
1:50- Léa; Papa, je veux encre la tête à-l'envers! (Daddy, I want head upside-down!)
1:54- Pilot; Oui! On y vas! (Yeah! Getting there!)
1:57- Léa; Tête à-l'envers... (Head upside-down...)
2:08- Léa; Encore! ... (Again!...)
2:08- Pilot; OK! (OK!)
2:08- Léa; ...Encore! (... Again!)
2:11- Pilot; Oui! (Yes!)
2:13- Léa; Encore! (Again!)
2:23- Léa; ENCORE! (AGAIN!)
2:28- Pilot; Ça vas? (Still right?)
2:29- Léa; Encore! (Again!)
2:31- Léa; Encore! (Again!)
2:32- Pilot; Oui... on se repose deux minutes... d'accord? (Yeah... we take two minutes... OK?)
2:35- Léa; Encore la tête à-l'envers. (Head upside-down again.)
2:27- Pilot; Oui? On vas se reposer? On remonte... (Yeah? Do we take a break? We'll climb-up...)
2:39- Léa; Encore. (Again.)
2:40- Pilot; ... on remonte un p'tit peu. On en refait une fois puis on atterri. (... we climb-up a little bit. We do it one more time then we land.)
2:48- Léa; La tête à-l'envers! (Head upside-down!)
2:49- Pilot; On fait pareil? (We do the same?) Léa gives a "thumb-up".
2:53- Pilot; Et c'est parti! (And here we go!)
3:02- Léa; Tête à-l'envers! (Head upside-down!)
3:11- Léa; Encooooore! (Agaaaaaain!)
3:22- Léa; encOOOOOre! (agAAAAAAIIIIn!)
3:28- Léa; Encore! (Again!) (by now, you must have a good idea of the meaning of "encore" :

:...)
3:35- Léa; Encore! (do I really need to spell it out?)
3:30- Pilot; Voilà! C'tait bon? (That's it! Was good?)
3:43- Pilot; Maintenant, on vas atterrir. (Now, we're going to land.)
3:45- Léa; Encore! (what else...)
3:47- Pilot; Une prochaine fois Léa. (Next time Léa.)
I left the laughter aside as they are pretty much international.
I saw a piece on the news on TV last evening. As you may have guessed, the pilot is Léa's father. He was a military pilot and has a license to teach aerobatics. Mom was a flight attendant.
This was not Léa's first flight; at 3, she went with her father under the strict condition (imposed by Mommy) that no inverted flying would take place. Now that she's 4, she can take it! Don't you think?