Following the death of our mother, my brothers and I found ourselves in joint ownership of a property. As one of them had debts, his creditor applied to the courts for the property to be divided up, [...]

 [...] leading the judge to decide that the property should be sold by auction. Is there any way to prevent the property from being sold at auction?

Yes, article 815-17 of the French Civil Code stipulates that when the personal creditors of an undivided co-owner initiate partition, "the co-owners may halt the course of the partition action by discharging the obligation in the name and on behalf of the debtor. Those who exercise this option will reimburse themselves from the undivided assets". This means that you can avoid having to sell your property at auction by reimbursing your brother's creditor for his debt.