I found this movie delightful. It is the most Wes Anderson of Wes Anderson movies. Effectively a paean to the halcyon days of the New Yorker under William Shawn it doubles as a love letter to the written word, the literary written word. I love movies like Wes Anderson makes, and to a lesser extent the Coens, that are forthrightly self-conscious about their storytelling. In a sense, there is no need to suspend disbelief here because belief in the film as representative of reality is never intended.
Another thing I love about it is how it is all done in the service of the personal. Love, grief, loneliness, resentment, aspiration, family -- the motivations of the characters are almost exclusively personal. One particular section that is set during the Paris student uprisings in the 60s seems to explicitly belittle any political notions. The acting is as wonderful as you would expert given the hi-end cast. A stand-out among stand-outs being Jeffery Wright as Roebuck Wright.
The audience that appreciates humanity and the written word over socio-political motivation and basic exposition is dwindling fast. We have to be grateful for every breath of fresh air we get. I hesitate to recommend this movie to anyone. The vast majority of people would find it merely curious, or worse: boring. Most movies are positioned for the largest audience possible. The French Dispatch is positioned for me.