Stanislas Guerini, who helped found President Macron's centrist movement in 2016, threatens to pull back support for Sara Zemmahi, who is running for office in the southern city of Montpellier.
Thousands marched in Paris and cities across France carrying banners with slogans such as "Police everywhere, justice nowhere", and "State of emergency, police state."
Officials in the southern city of Montpellier said around 2,000 people gathered in the city centre — organisers put their numbers at closer to 5,000.
President Emmanuel Macron's Republic on the Move (LREM) party won a resounding majority in the national parliament after a historic victory, indicating a major shift in the French political landscape.
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