I'll admit from the start that you won't learn anything from reading the words that follow. Celine and Julie Go Boating is a cinema classic. It is #213 on the They Shoot Pictures, Don't They list of the top 1000 films of all time. It was tied at #122 in the poll of TSPDT users that was posted a few weeks ago. More than once, critic David Thomson has called it his favorite film (that's when he's not calling it the "The most radical and delightful narrative film since Citizen Kane").
On the other hand, the heading for one of the articles I linked to read "A film you may want to walk out on --- but only for a while". And there is an oft-told and perhaps true story of a festival screening of Celine and Julie Go Boating where Pauline Kael is said to have stood up halfway through the movie, grabbed her coat and hat, announced to the audience "I'm going to the movies!", and walked out.
I encourage you to check out the many fine essays written about this film. Thomson writes about it in his book Have You Seen...? Beatrice Loayza has a solid piece that can be found on the Criterion website.
But I have nothing to say. Celine and Julie Go Boating is 3 hours and 13 minutes long, and I don't think I understood what was going on for at least three hours of that running time. There are movies, usually from other countries but at times just about cultures where I am an outsider, where I miss context, and find it useful to look up information about the country or the culture to help me better understand what I have seen. With Celine and Julie, I was so lost, I found myself looking online for anything that might explain the movie to me. I had nothing to hold onto.
While at times the frustration I feel makes me intensely dislike a movie like this, I try to recognize when a film isn't a failure, despite my confusion, but the result of a film maker's vision. Celine and Julie Go Boating is likely the exact movie director Jacques Rivette and stars Juliet Berto and Dominique Labourier wanted. There's a reason the film is considered a classic. I'm just not sure I ever want to see it again.
If you need signposts, Celine and Julie is often cited as a precursor to Mulholland Dr., a movie I didn't like. It clearly influenced Desperately Seeking Susan, which I haven't seen for a long time:
It's often compared to the 1966 Czech movie Daisies, which I loved. And at times it reminded me of Last Year at Marienbad. If you liked any of those movies, you might consider seeing Celine and Julie Go Boating.