Emmanuel Macron has made a number of policy concessions following the "gilets jaunes" protests which rocked the country.
On Monday night, Mr Macron addressed France for the first time since anti-tax protests around the country turned into rioting in Paris.
The French president acknowledged "anger and indignation" among the public over the cost of living, even describing himself as partly responsible.
But Mr Macron promised "all means" will be used to restore calm, adding that "no indulgence" would be given to people behind the protest violence.
He said "no anger justifies" attacking police or looting stores, saying both threaten France's cherished liberty.
During his address, Mr Macron promised to speed up tax relief for struggling workers and to scrap a tax hike for retirees.
He reiterated earlier promises to raise the minimum wage and pledged to abolish taxes on overtime pay starting on January 1, several months before schedule.
He also said a tax hike on pensioners would be scrapped.
All of the measures had been demanded by the yellow-vested protesters who have led four weeks of increasingly radicalised demonstrations against Mr Macron’s presidency.
Mr Macron acknowledged being partially responsible for the anger that fuelled the protests, saying: "We probably have not been able for a year and a half to bring quick enough and strong enough responses."
He also acknowledged he may have given an impression "not to care" about the concerns of ordinary citizens and "might have hurt" some people with his comments.