This is the title of a new film that was reviewed in today’s Los Angeles Times. Does the title make you wonder if the pronoun is correct? In fact, it depends what the filmmakers wanted to say.
“Dior and I” is correct if you are using “I” as the subject pronoun it always is. For instance, “Dior and I collaborated on many shows.”
But “Dior and Me” would be correct if you’re using “me” as the object pronoun it always is. For instance, “The Winter 2000 show was produced by Dior and me.”
If you are uncertain about when to use “I” and when to use “me,” I hope this helps.