1. OP is free to leave AA if he wishes. These same errors occur over at UA & DL, so he'll either be back or unhappy elsewhere.

2. Those recommending a DOT complaint haven't read the DOT rule. There is not enough information in OP's post to determine whether a DOT violation ocurred. That is based on OP's e-ticket confirmation. He needs to look at that. If he shows an e-ticket for the itinerary at $1,500, that is price, AA must honor it and just like mistake fares, eat the error out of its revenue. If his e-ticket is only for part of the itinerary, that is what the $1,500 covers. Anything AA offers to mitigate that is a customer service gesture only and not required by DOT.

3. As to "what should I do"? Again, the "complain to DOT" crowd aren't offering helpful advice. OP needs to get back from CDG where he won't be boarded without a ticket. He has no option but to pay the add/collect. Upon his return and conclusion of the itinerary, he should then evaluate #2. If a DOT complaint is appropriate, DOT will require AA to document what happened and that will either result in AA admitting an error and refunding OP the add/collect or AA sticking to its guns (as it usually does) and, if DOT rules against AA, ordering AA to refund the money and possibly fining AA if this is a pattern.

The key right now for OP is to find his e-ticket receipt(s) and make sure that he has a ticket as he believes he does for the price he paid.