Oh man, French film is my spirit animal! And no, I don't have a letterboxd, but I just googled it and it looks like something I want to have lol I suppose you have one?
Oh lord, where to begin?? First thing you need to watch, is Breathless by Jean-Luc Godard. This is posterchild movie for the French New Wave and is responsible for influencing countless other filmmakers and new wave movements (Czech new wave, American new wave,etc.). Wes Anderson is a HUGE fan of the French New Wave, so if you want to see many of Anderson's influences just dive into this era (late 50's to mid 60's). I am happy to write a bigger list of New Wave must-see films if it interest you :) Other phenomenal French films. Blue is the Warmest Color directed by Abdellatif Kechiche. This 3hr drama centers on Adèle, a 15 yr old discovering her sexuality. This film won the Golden Palm at Cannes in 2013 and is a beatifully shot, emotional and moving story. Highly recommended and my favorite of 2013. Irreversible by Gaspar Noé is a very interesting film dealing with time, revenge, and love. Starring Vincent Cassel (of La Haine fame ;) ) this movie tells the story of a man seeking revenge in reverse order. One of my all-time favorites. Disclaimer: This movie is violent and there is a disturbing rape scene which may be hard to watch. If you are a fan of horror or gore, then check out French New Extremism!!! A movement from the late 90's to mid 2000's featuring lots of violence. My favorite films from this movement are Inside, a home invasion movie that is badass and scary, and Martyrs. I cannot recommend Martyrs highly enough, it is brutal, thoughtful, mindbending, and actually has a good amount of brain food for a horror movie. Honorable mention is Haute Tension a slasher flick with one hell twist. If you want something back on the artsy front, check out the Three Colors trilogy!!! Made by a Polish director Krzysztof Kieslowski (say that 3 times fast!) but the first and 3rd parts are in French because France helped produce the films. This trilogy is absolutely amazing, and has some great performances, my fav being Juliette Binoche. For a weird Sci-fi type go check out Mauvais Sang from Léo Carax. It tells the story of near-future Paris where an AIDS like virus is infecting people who have sex without being love (gasp!). Or you could watch Carax's most recent film Holy City Motor which is one of the weirdest but most fascinating releases of the past few years. These are only a few suggestions, lemme know what you like or what genres you'd prefer and I could probably help out more :D
Blue is the Warmest Color is an incredible film, it's unsettling at times but I really enjoyed that. I need to add everything else on your list as I haven't seen it. La Haine is great, Amelie is great, but there's one set of films that I can't help but but-in to recommend to Zurangatang in addition to yours: Jean de Florette and Manon des Sources, these two films star Gerard Depardieu and Yves Montand, two of the most notable actors in the history of French cinema. It's more of a period piece than anything else, but the acting, dialogue, and settings are incredible. It revolves around the tension between rural and urban France, when a taxman decides to take up farming in rural France and is faced with opposition from two traditional rural Frenchmen.