The case comes amid heightened racial tensions following the jihadist killing last week of French teacher Samuel Paty, who become the target of an online hate campaign after showing his pupils cartoons of the Prophet Mohammed.
The women accused over the assault were drunk when they came across a group of Muslim women and children in the Champ de Mars park at the foot of the Eiffel Tower.
The Muslim family complained about the other women's dog, saying they felt threatened by it.
In the ensuing row one of the women with the dog pulled a knife and stabbed two of the headscarf-wearing women, aged 19 and 40.
The 40-year-old woman sustained six stab wounds and is being treated in hospital for a perforated lung.
The younger victim was stabbed three times and was also treated in hospital but has since been discharged.
Both victims claimed their attackers called them “dirty”, used racial slurs and told them: “This is not your home.”
The incident caused a furore on social media with some people accusing the French media of remaining silent about an attack they saw as clearly anti-Muslim.
The main suspect has been placed in preventive custody while her friend has been released on bail, sources close to the investigation said.
The pair were charged late on Wednesday with assault aggravated by the use of a weapon, drunkenness, racial insults and the fact that they acted together.
But the victims' lawyer Arie Alimi has called for the women to face stiffer charges, accusing them of attempted murder linked to the victims' race or religion.
He said one of the women specifically took issue with the headscarves worn by several women in the Muslim family, referring to it as “that thing you have on your head”.
He also accused the suspects of trying to rip off their victims' scarves and of aiming blows at the head.
The two suspects deny making racial insults.
Their lawyer Bernard Solitude warned against “blowing this story out of proportion” and said it was important to “stick to the facts: a row which degenerated after insults were made”.
Alimi accused the French authorities – which have closed a mosque on the outskirts of Paris and moved to shut down several Muslim groups in the aftermath of the beheading of teacher Samuel Paty by an 18-year-old Chechen radical – of a “witch hunt”.
He argued it had the effect of helping jihadists “reach their goal, which is the stigmatising of Muslims leading to more individuals becoming radicalised”.