Centrist politician Borne succeeds Jean Castex as France's prime minister, becoming the second woman to hold the post in the country.
Prime Minister Jean Castex says conclusions can't be drawn on the April 24 runoff at this stage, adding that "we have to convince the French that Emmanuel Macron's programmes are the best for France".
Inspired by Canadian truckers paralysing border traffic with the United States, the demonstrators include anti-Covid vaccination activists and people angry at fast-rising energy prices.
French President Emmanuel Macron argues the legislation is needed to shore up his country's secular system, which many fear will stigmatise French Muslim community, Europe's largest.
Protesters clash with police as tens of thousands rally against state violence and a controversial bill that would restrict sharing images of law enforcement officers.
The attacker fled the scene after the shooting outside the church in Lyon, seriously wounding a Greek Orthodox priest, police said earlier.
Jean-Francois Ricard, France's chief anti-terrorist prosecutor, said the attacker was a Tunisian born in 1999 who had arrived in the Italian city of Bari on October 9.
The 18-year-old said he wanted to avenge the republication of cartoons of the Prophet Mohammed by the satirical weekly, which in January 2015 was targeted in a massacre carried out by gunmen.
Fourteen suspects face charges including financing terrorism, membership in a terrorist organisation and supplying weapons to the attackers that killed 12 people in 2015.
The relatively low-profile Castex replaces Edouard Philippe, who resigned earlier in the day. Macron is reshuffling the government to focus on restarting the economy after months of lockdown.
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