Giorgia Meloni called the medal, and a 100,000-euros ($113,000) donation Paris City Hall made to a separate French-based migrant-rescue organisation, “new, intolerable provocations by Paris”.
A group of around 20 members of Meloni's Fratelli d'Italia (Italian Fraternity) party demonstrated outside the embassy as prominent Italian political turned up.
The medals were being awarded to Carola Rackete and Pia Klemp, the female captains of the Sea Watch 3 ship that, under Rackete's command, last month sailed migrants past a police blockade into a port on an Italian island. Rackete is facing legal action in Italy over the incident.
The donation was made to SOS Mediterrannee.
Relations between France and Italy are frayed over a number of political differences, among them the populist, hardline policies of Rome on the arrival in Italy of asylum-seekers.
Italian Interior Minister Matteo Salvini on Twitter accused France of “hypocrisy” over the Sea Watch incident, alleging its authorities did not respond to appeals for assistance by Rackete as she sought a port to offload the 40 rescued migrants on board.