For the record: Jean Valjean did in fact commit breaking and entering, two burglaries (though one victim refused to press charges), at least four prison escapes, highway robbery (technically), parole violation, faking his own death, trespassing, and identity fraud.
Javert isn’t chasing an innocent man on false evidence.
Valjean’s role isn’t to show persecution of the innocent, but of the redeemable. It’s to show that the justice system is excessively harsh. His time in prison for a minor crime makes him a worse person, actively turns him into a danger to society. Worse: the system actively undermines his efforts to reform and redeem himself afterward. In a humane justice system, he would have left prison years earlier, and been able to make his way again. Though it probably would have still been too late for most of his sister’s children.
Also worth noting: Javert isn’t trying to uncover Valjean’s crimes, or prove them. They’re well-established by the time he gets involved. Javert just wants to catch the guy so the system can grind him down again…because that’s what “law and order” means to Javert: punishing those who defy authority.
Update: On a related note, this tweet by @beesmygod provides a little perspective: