The girl, who died on Christmas Day, reportedly of sudden infant death syndrome, was refused burial in Champlan, south of Paris.
The mayor said priority had to be given to taxpayers.
The mayor of nearby Wissous, Richard Trinquier, described that decision as ?incomprehensible? and said that he would offer a grave.
The girl?s family lived in a camp in Champlan.
The mayor of Champlan, Christian Leclerc, was quoted by Le Parisien newspaper as justifying the decision by saying that his town was running out of burial space and that ?priority is given to those who pay local taxes?.
Local activists expressed outrage, with a spokesman for the regional association for solidarity with Roma and Romanians describing the decision as a case of ?racism, xenophobia and stigmatisation?.
Mr Trinquier, who is a doctor and had previously treated the baby?s mother, said he had accepted the girl as he would have accepted anyone else, since ?everyone has a right to a decent burial?.
The girl is due to be buried on Monday.
The presence of Roma people from Eastern Europe has been a hot political issue in France.
It has one of the harshest policies in Europe towards Roma immigrants, regularly demolishing the camps that many of them live in, and deporting thousands every year.
The majority of France?s 20,000 Roma live in makeshift settlements.