The shirt that Alizée is wearing in that picture and dance video are not the shirt she was gifted from the time she kicked the ball to start the season, simply her wearing a shirt that supporters can buy and pay to have their name added.
When she kicked off the season it was back at the time of her first album and the height of her fame/publicity campaigns. The shirt design then was different, still white and red, but a larger stripe. I can't find a picture of her wearing it, but here is the publicity photo of her holding it up showing her name on the back:
https://i.ibb.co/3Wsw3LG/temp-ajaccio.jpg
Credit to archiving that image geos to Aragorn97 :D It appears the old news stories related to this are no longer online :(
Alizée still very much supports AC Ajaccio, as does Annily, sadly in 2021 a young 17 year old player that was a family friend passed away and they both posted tributes to him.
Link to the news story
Despite being able to find several news stories in French about her attending matches and being a fan etc, I can't find any pictures of her wearing the shirt, though she obviously buys them to support the team. As football shirts are large and loose fitting, I imagine she perhaps wears them as loungewear/casualwear around the house or as a nightshirt, but then dresses up when going out in public and likely to be photographed. This would explain her wearing it whilst in dance rehearsal. I've had girlfriends in the past who around the house would wear sports shirts at home with no pants, like a dress or nightshirt (SO hot! :p ) but wouldn't be seen dead wearing them outside as they don't think they flatter their figure. Little do they know men find it sexy :))
Another team Alizée has links to is Lille. In 2016 she attended a charity event there for the National Union of Sport to raise money for helping young people train to become football players. She was gifted a football signed by the whole team, and performed several songs.
Link to the news story which has lots of pictures
That last one is especially interesting to me as Lille is just one train stop away from my apartment. I must admit I don't know much about there, I just pass through when on my way from/to London. I don't know much about French football teams, other than PSG of course. I should get an AC Ajaccio shirt for when I next visit Corsica :dance:
Edit:
Yes, congratulations to them! What an absolutely beautiful picture!