As above. That the man in the Iron Mask was real is well documented (Though the mask was likely velvet, not iron). His name is given in record as Eustache Dauger, a valet, and he was locked up starting in 1669 in assorted prisons where France normally kept prisoners embarassing to the State - people whose actions or information would look bad for the state or its allies. Known prisoners in the same prison included former Finance Minister Fouquet (who arrived in the prison before Iron Mask, so Dumas' timeline doesn't quite add up). His cell was poorly furnished (a typical jail cell, not the luxury granted prisoners of high rank), and while in prison he was made to act as valet to other prisoners.
That he was the brother of the king is unsustained and pretty much unsustainable, because any pregnancy (and giving birth) by the Queen would have been a very public event, attended by members of the court. A secret child born from the Queen is just very hard to fit in (though it does make for good stories), though a twin is just barely technically possible (Louis XIII dragged the court to a religious ceremony after the birth...so if there was a protracted second birth they might, maybe, just have missed it. This remains extremely unlikely.
A royal *bastard* is more in the realm of the technically possibile (Though not at all likely), which normally wouldn't pose much of a succession challenge but there were lots of rumors about Louis XIV's own legitimacy. Unfortunately, as fun as that theory is, Louis XIII is not only not known to have had any bastards, he's not know to have had any *mistress*, female favorite or any such thing. Whatever he was (there is some debate), heterosexual probably wasn't it, and bisexual doesn't sound too promising either. Others have suggested that the bastard in the story is indeed Louis XIV - and that his natural father was the one in the mask.
Much more likely, Iron Mask was a fairly low rank person, but one associated with people of higher rank, and perhaps fairly recognizable despite the low rank - possibly someone whose presence in prison would have implicated people of much higher rank than him in unsavory things. Certainly, lots of unsavory things were happening in France at the time - the decade before Dauger surfaces is the Fronde, the decade after is the Affaire des Poisons - and there may have been more that we don't have records of. Or the arrest may even be a precursor of the Poisons (there is even some indication that a man named Eustache Dauger de Cavoye may have been implicated in the affair of the poison, but again Iron Mask was already in jail by then, and there is evidence Dauger de Cavoye and Iron Mask were imprisoned in different prisons at the same time. One certainly suggestive development in 1669, at the time of the crime, is the execution of Roux de Marcilly, a Huguenot who orchestrated a major plot to overthrow Louis XIV - Iron Mask may have been a man linked to the plot in some manner.
Or Iron Mask could be a conflation of multiple prisoners whose history and need for secrecy makes it impossible to tell which one is which.