One 29-year-old man was found dead in the northern city of Douai on Saturday and two others died on Sunday, one 50-year-old man in Paris and a Belgian 46-year-old in south-eastern France.
All three apparently died of hypothermia, according to authorities.
After an unusually warm spell of weather, France has been gripped by a sudden freeze in the past few days, with the mercury dropping to minus 14C (7F) and as low as minus 22 in the mountains.
French authorities said they had offered the 29-year-old man emergency accommodation but he had "systematically declined the offer".
The 50-year-old Parisian had also been approached by authorities. He was found in a state of hypothermia and died when receiving first aid.
The Belgian man's death was "due to cold" but he was heavily under the influence of alcohol, authorities said.
He lived in a tent with his mother, who came from Belgium to look after him.
Meanwhile the charred bodies of two homeless men were found east of Paris on Tuesday. Police said they had apparently lit a fire in a condemned building where they were sheltering from the cold.
In 2013 a total of 453 homeless people died on the streets of France according to a memorial book compiled by campaign group "Les Morts de la Rue" (Dead in the Streets). The shocking figures, which were released in March, showed that a person living on the streets dies every 20 hours.
Christophe Louis, the president of Les Morts de la Rue, told The Local at the time that the figures were "shocking" and the goverment must act.
"It's a scandal," said Louis.
"The French government needs to introduce a series of reforms aimed at providing help for those on the street. They need access to lodging, for a start, and financial help," he said. “They need to protect the country’s most vulnerable.
The average age of the homeless dead - some of whom have proved impossible to identify and are included in the book simply as "a man" or "a woman", was below 50. That stands out when compared with the fact that average life expectancy in France is 81.5 years.
Some 141,500 people were without a fixed abode in France in 2013, according to a report by national statistics agency INSEE. More than 30,000 of those were children.
This number represents a close to 50-percent increase in homelessness in Europe’s second-largest economy since 2001.