The "Nowhere but Out" report comes amid tensions between France and Italy over French President Emmanuel Macron's criticism of Rome over its rejection of a migrant ship carrying 629 people rescued from the Mediterranean.
Oxfam said some 16,500 refugees and migrants -- a quarter of them unaccompanied children -- passed through Ventimiglia, a small town about seven kilometres (four miles) from the French border, in the nine months to April.
The report said children complained about being "physically and verbally abused, and detained overnight in cells without food, water or blankets and with no access to an official guardian," all contrary to French and EU law.
Oxfam staff and partners said there were cases where border guards cut the soles of the shoes of child migrants or stole their phone SIM cards.
"In one case, a very young Eritrean girl was forced to walk back across the border along a road with no pavement carrying her 40-day-old baby," it said.
Most of the migrants were fleeing persecution and war in countries such as Sudan, Eritrea, Syria and Afghanistan.
Many of them are trying to reach other countries like France, Britain, Sweden and Germany where they hope to join relatives or friends.
"Since France tightened border controls in 2015, thousands of people have been stranded in Ventimiglia without sufficient assistance or access to basic services," Oxfam said.
"Hundreds of refugees and other migrants sleep rough under a flyover, with no access to drinkable water, shelter or heating."
'Pushed us off the train'
"French police officers are not upholding international standards. They taunt children and mistreat them.... Some children have had the soles of their shoes cut off before being sent back to Italy," said Chiara Romagno, Oxfam's OpenEurope project leader in Ventimiglia.
"The resolution of people to reach their loved ones in other countries, and the lack of sufficient safe and regular pathways to do so leaves them no choice but to try until they succeed," Romagno said.
Michael, a 15-year-old from Sudan's troubled Darfur region, said he and a friend tried to enter France but the "police pushed us off the train.
"Then they pushed us in a van in the railway station car park. We were given a document (refus d'entree, refusal of entry) in the van and we were put on another train going back to Italy, without any explanation."
The report said Roja Camp, the official camp set up outside Ventimiglia, was vastly overstretched and that the "heavy police presence at the entrance and compulsory fingerprinting deter many from staying" there.
Most migrants preferred to live rough, sleeping under a motorway outside town with no sanitation facilities or clean water.
"In Ventimiglia, there are no arrangements to take care of the returned children. Once off the train, they are left to fend for themselves," the report said.
Oxfam said France should immediately stop and adequately sanction the "illegal practices of the French police at the French-Italian border", ensure the right to seek asylum for all foreign children in French territory and take care of them according to the provisions of national, European and other international laws.
An EU scheme to distribute migrants equitably around the bloc has failed miserably, with central European members flatly refusing the quotas and others, including France, falling far short of their allocated target.
Italy has received more than 700,000 migrants and refugees since 2013. Many West Africans try to continue on to France, where they speak the language and often have relatives, only to find the border shut to them.
Thousands of those who manage to sneak across the Alps have been detained and sent back to Italy.
By Abhik Chanda