They would probably be dressed like nuns, because that's largely what they were (Catholic Sisters of Charity, at any rate). Here are some examples of 1850s habits. The Sisters would be wearing the typical black serge gown with white headdress.

Nursing as a modern profession emerged in the latter half of the 19th century. Florence Nightingale set up the first secular nursing school in London in 1860. Prior to this, women serving the sick in this capacity were just natural caregivers doing what felt right, what experience had taught them would be a comfort, or what the doctors instructed them to do. There wasn't any formal training. There weren't any uniforms, because this wasn't really a profession - more a specialized function of other work. For example, these Catholic sisters (and Protestant deaconesses) were that first, and then they served this role. At home (where the majority of care took place), we find basically a specialized type of servant - the chamber nurse. (Servants wore plain long dresses in drab, dark colors.) Most home nursing was done by regular people, though.

I'm not entirely sure where to point you for sources of more information, because the history of nurses in France doesn't begin until 1870 or so. The Catholic Sisters were the predominant figures in hospital care before that, and what they were doing was definitely care and maintenance, not modern medical practices. You can read about Florence Nightingale's experience with the French style of hospitals in her Subsidiary Notes as to the Introduction of Female Nursing Into Military Hospitals, 1858. She studied with both the Sisters of Charity in Paris and the Protestants at Kaiserwerth in the 1850s so her perspective is well-rounded. I'm afraid I don't know enough about Catholic religious sisters to offer any sources for accounts of their lives and experiences.