I am sorry to learn of this situation.
The statute of limitations for breach of written contract in Louisiana is 10 years. This means that the lender can pursue you for the deficiency (the amount of the loan minus what they were able to auction your car for (minus costs of repossession and sale) for up to 10 years after you defaulted on the loan.
Make sure that you have filed an answer to the complaint with the court. If you fail to do so, you will lose your case "by default" (they will get a judgment against you for the full amount they are asking for and you will lose the opportunity to defend the matter on its merits). Even if you are trying to settle the case - make sure you file an answer.
For help with this, visit your local self help center (usually at your courthouse or law library), or see: http://www.creditinfocenter.com/legal/affirmative-defenses.shtml for general help.
You are wise to try to settle the matter with the other party (both sides generally win if they can reach a settlement).
When trying to settle a debt, creditors generally prefer lump sums over payment plans. They are often willing to accept an amount less than the full debt (the trade off is that they get a quick payment and don't have to worry about ongoing collection costs or administration). If you do not have the ability to offer a lump sum for something the creditor will accept (some will accept a small portion, while others want close to the full amount), you can try a payment plan, these are less satisfactory to the creditor (especially if they have a lien on your property already), but if you are willing to offer something with a reasonable chance to get the creditor a large amount of their debt back, you are likely to get them to accept it.
Whenever working with a creditor, make sure that you keep your communications in writing (if you speak to someone by phone, promptly send a confirmation letter to summarize your conversation), as this will help to ensure that there is no confusion later on, and you will be able to enforce your settlement against any future collection efforts.