The marble was bought from dealer Bowman Sculpture last year.
Originally priced at £280,000 by the gallery, a discounted final purchase price was agreed with the museum in Nogent-sur-Seine, 60 miles south-east of Paris.
Sculptor Boucher (1850-1934), a mentor to artist Camille Claudel and a friend of Auguste Rodin, conceived the work in c.1894-96 and it was completed in 1897.