No. This is Likely a Conflation of Batman’s Three Musketeers Origin With Other Notable Works by Alexandre Dumas
1. Bob Kane’s inspiration: like many old comic book characters, there are legal and copyright questions about who created Batman. First, we absolutely know that Bob Kane created Batman, because DC has record of his original contract, which names him sole creator:
Bob Kane has stated on several occasions that his inspiration for Batman:
Inspired in equal measure by Leonardo da Vinci’s 1485 design sketches of an “ornithopter,” a 1930 mystery movie entitled The Bat
Whispers, and the 1920 silent film The Mark of Zorro starring Douglas Fairbanks, the commercially savvy Kane managed in short
order to assemble the Bat-Man “from an assortment of pop culture debris that together transcended the sum of its parts”
The Count of Monte Cristo has never been any published inspiration for Bob Kane, and therefore, if one accepts Kane as sole creator, then Batman is not inspired from the Count of Monte Cristo.
2. Questions About Who Created Batman
Enter Bill Finger. Bob Kane himself admitted it was a mistake to not credit writer Finger in the many years he maintained sole creatorship. Kane himself, over the course of his life defended himself against “conjectures,” “misrepresentation,” and “distortions of the truth” and expressed misgivings about his business arrangement with Finger. However, more recently, Kane has lamented that:
“I always felt rather badly that I never gave him a byline,’ said Kane recently. ‘He was the unsung hero’”
Assuming, therefore, that Kane himself admits Finger contributed to the narrative creation of Batman, then Finger’s own inspiration enters the picture.
Bill Finger has in past stated his inspiration for Batman. From Batman: The Complete History, [San Francisco: Chronicle Books, 1999, Finger reveals that he:
“further fleshed out the character, whom he saw “as a combination of Alexandre Dumas’s swashbuckler D’Artagnan from The
Three Musketeers (1844) and Sir Arthur Conan Doyle’s detective Sherlock Holmes” and wrote countless Batman scripts in the
years that followed.
Consequently, Finger also has not explicitly connected Batman’s creation to the Count of Monte Cristo. However, Finger identifies another Dumas work, The Three Musketeers.
So we know that the creation of Batman was based on several inspirations. However, one of those inspirations has not explicitly been revealed publicly to be the Count of Monte Cristo.