France is a free country, so you can basically do as you please, and a flash mob shouldn't be an issue anywhere in a public setting.
However, if you want to stick to the letter of the law, this would probably be considered a public reunion, which may require authorisation from the "Préfecture". Also, the use of music in a public setting normally implies getting the authorisation of the rights holders and/or paying them fees. But I doubt you would have any serious issues with either of those in this specific context.
On the other hand, remember that France is under high-level alert (actually in the "Etat d'urgence" situation, which is basically just one notch below a state of war), and anything that might look suspicious may get you into trouble, especially in a high-profile "target" such as this (with lots of people and tourists), which is likely to be filled with cops and soldiers bearing arms.
I would recommend at the very least finding cops on site and notifying them of what you intend to do beforehand so they're not surprised when they see lots of people apparently preparing something.