Is it permissible for the questioner's relative to sell goods at a higher price than she bought them for, given that the questioner's friend asked her relative to buy these goods from France, and agreed to the increased price?

If someone commissions another person to buy an item, it is not permissible for the agent to increase the price for the principal in order to take the difference for himself without the principal's knowledge and consent, as this is deception forbidden by Islamic law. However, it is permissible for the agent to stipulate a known fee for his agency. If your relative increased the price of the item for which your friend commissioned her to buy, and she told her a price other than the real one, then this is not permissible except with the friend's knowledge and consent.