1.Fruits Basket: Both are stories that are romances at heart but take a really long time for the main couple to get together and both of those relationship starts off as friendships. The characters in both stories are well developed although I believe the ones in Fruits Basket are more developed but that series is a lot longer so they have more time to develop. Also in both stories there's the idea of home being a person present in Anna and the French.
2. Cardcaptor Sakura: I've notice that a lot of people love Anna and the French Kiss being a sweet Innocent love story and well you can't find a love story more sweet and Innocent than Cardcaptor Sakura. While Anna focuses mainly on romantic love with a dash of friendship Cardcaptor Sakura covers all forms of love first crushes, friendship, family, unrequited, and romantic.
3. Shiver: I think this books are similar due to the description in scenes were the main couple shares a bed since in both it's described in a way that just feels so intimate. I also think that both series main couple shares a really emotionally intimate relationship as well.
4.I'd Tell you I Love you but Then I'd Have to Kill you: Both series are about falling in love for the first time and are set at boarding school. I also think both of them are written with a fun narration.
5 and 6. How to be Popular and Pants on Fire: The writing style in these books are super fun and helps you to understand who the main character is really well which is the same as with Anna and the French Kiss.
7.The Darkest Powers series: Both main characters love film and want to be involve with the industry as a job some day, I'll admit this one is a bit of a stretch.
8. Clannad: In both stories the main guy helps the main girl come out of her shelf a bit and there's lots of friendship and romance in both.
9. Heist Society:There's a great main character, a swoon worthy guy, an awesome group of friends and plenty of descriptions of European cities which all seem to be things that people also loved about Anna and the French Kiss.