Door grill in the Marais, rue des Archives.

This is the kind of hat you will find on Marianne.  Marianne is an image of a woman that is supposed to represent France. The little ribbon on the side of the hat would be in red, white and blue and symbolises the revolution.

mariefrance

Does anyone have any information on the star and lightning bolts? (Update: Read the comments section for the symbols explained by Marjorie)

star