A few years ago, my mother signed a mandate for future protection and appointed me as her proxy. Today, she seems to be losing her memory and isn't always aware of what she's doing. How do I go about implementing this measure?

If it appears that your mother is no longer capable of looking after her own interests, you must inform her of your intention to implement the mandate. Her condition must then be certified by a doctor chosen from a list drawn up by the public prosecutor. This medical certificate and the power of attorney must be presented to the clerk of the court in the place where the mandator (in this case, your mother) resides, who, after checking that the conditions have been met, endorses the power of attorney, and returns it to you.
After obtaining the latter, you will be able to implement the mandate (art. 481 C. civ. and 1258 C. proc. civ.).