In a new political development, a 31-year-old nurse named Ingrid Levavasseur said this week she would lead a yellow vest list of candidates for the European elections in May.
Mr Rodrigues, 40, a building worker, told BFM TV he believed the police had targeted him deliberately while he was filming the demonstration.
Meanwhile, hundreds marched through Paris wearing red scarves on Sunday to protest the unrest that sometimes plagued the Yellow Vest movement as the "Red Scarves" and "Blue Vests" launched joint counter-demonstrations.
"I think we will come out of this debate only with very strong, powerful decisions, because we need them", Macron said during a recent exchange with a group of mayors and "yellow vests" in the southeastern commune of Bourg-de-Peage.
Thousands of protesters have marched through Paris to condemn violence in the "yellow vest" movement that has rocked France for weeks.
John Christophe Werner from the southern French region of Vaucluse founded the Red Scarves movement on Facebook.
Baptiste Baudrin, a Red Scarves member, says he will march in Paris on Sunday because the Yellow Vests have turned "anarchist and extremist".
Around 69,000 people attended the latest Saturday protests, including 4,000 in Paris, a lower turnout than the previous weekend, the interior minister said.
3-year-old boy goes missing from grandmother's backyard
The young boy's family said he appeared in good spirits and was already asking to watch television. "The terrain was woods". The family of a 3-year-old boy from North Carolina claimed that he was protected by a bear while missing for three days.
A prominent anti-government "yellow vest" activist was badly injured in the eye after being hit by a rubber bullet used by the French police, his lawyer has said.
Rodrigues was injured at Place de la Bastille on Saturday afternoon, during an 11th weekend of demonstrations by the gilets jaunes in Paris.
Multiple anti-government protests took place in Paris and other cities, centred on Macron policies seen as favouring the rich. France deployed about 80,000 police officers to patrol the events and to disperse trouble.
He said he had agreed with Eric Drouet, another leading figure in the movement, to launch a "call for calm" while at the same time pressing on and strengthening the protests "without violence".
The devices - which are not used in most European countries - have become deeply controversial in France since the protests began in November, blamed for dozens of serious injuries.
Small groups of protesters at Bastille formed makeshift barriers, lit fires and threw projectiles at police, who responded with tear gas and water cannon, television footage showed.
Witnesses are reported to have picked up the projectile that struck Rodrigues and handed it to investigators.