Hi,
Sorry for taking time to reply.
Better to confirm with the consulate, but in general a proof or funds can be substituted by providing an affidavit of support. Be sure to have your signature notarized (a clerk at your local bank can help with that). It is also likely that the French consulate in Russia will require so called "apostille". Apostille is a confirmation from a state official that the notary who notarized your signature is real and valid. The apostille is usually provided by the Office of the Secretary of State.
In regards to the application process, whether delivering Schengen visa application in person is required, it is hard to say, you or she needs to contact the embassy at her place. There is no common way of administering Schengen visa, the process varies by country. And Russia is a bit different country, but I am sure you already know that.
Cheers.
Dani