Here's why:
* Pronoun Case: When used as the object of a preposition (like "of" in this case), you use the objective case of a pronoun. The objective case of "I" is "me".
* Subject-Verb Agreement: While "Jane and I" is correct as a subject, "Jane and me" is correct as an object.
Correct: "He was a former friend of Jane and me."
Incorrect: "He was a former friend of Jane and I."