The phrase "slimmed-down" is figurative. It means the public image of Hollande has been refined, with any unnecessary parts cut away. Think of "streamlined". Do not take the phrase literally. Grammar check: "PS. I know what 'slim down' is." You're not asking a question, so don't use a question structure.

I am assuming Hollande is a person. In that case slimmed-down would mean "less fat than before." So you could say: "Hollande, less fat than before and cultivated in a way the French like their presidents to be cultivated, should prevail." But it is more appropriate to say slimmed-down because using the word "fat" can be rude.