I've found a couple of other paintings by Renoir from 1885 and 1888 respectively, which feature the same setting(and woman?):
Seated Nude (also known as At East) - 1885. Pierre-Auguste Renoir (1841-1919) ? download painting ? Gallerix.ru
The Coiffure - 1888. Pierre-Auguste Renoir (1841-1919) ? download painting ? Gallerix.ru
At the bottom of the following Renoir Authentication Website's page there is a painting identical to yours which was attempted to be sold on ebay and classified as a fake.
Taken from this page:
"
Many of the Renoir impressionist fakes we see at Freemanart (and we see a lot) are actually mistaken as copies of original Renoir paintings and drawings or in some cases, proportionate parts of them.
However, deliberate forgeries, in the guise of Pierre Renoir painting and drawing fakes are oftentimes compilations of other known Renoir works, a favourite ploy of both the modern day forger and historical faker of art work .
This newly created Renoir fake work of art then magically becomes an 'unknown' or 'forgotten' lost Renoir painting, whereby the faker has taken images or elements from within other works of art known to be by Renoir or any other artist they intend to counterfeit and cleverly introduces and manipulates those elements into a brand new composition or work of art purportedly by that artist.
This process is always designed to deceive and defraud the individual and it's money and money alone which is the catalyst in the crime.
Another favourite scam with Renoir fakes and forgeries is to use an image taken from within one of Renoir's known legitimate works of art and invent new studies in paint or crayon or sometimes pastel to make us believe that this is a previously undiscovered Renoir study which has recently come to light. This is much more believable than a fully fledged masterpiece suddenly turning up and my word, there's a lot of them around!"
Also, Christie's offer a free appraisal service, so perhaps they would consider authentications as well?
Best of luck!