What order of nuns ran the french hospital in Manhattan in the 1940s?

I believe you are referring to Nursing Nuns at St.Vincent"s hospital in the Village. They were probably of the Sisters of Charity ( co founded by Vincent!) but there may be another order involved. There was a predominatley French order of Sisters of Ste Jeanne D"arc and these WERE associated with Saint Vincent"s Church- which is patterned in part on the famed French Madeleine- the Veterans of Foreign Wars chapel is well worth a visit! There is, of course a neat statue of the Maid-at-arms on the altar wich was brought over from France on the Normandie steamship in l935. So it is quite a famous church and a French language parish- in MANHATTAN.