Absolutely, but you'll need to get in touch with a Russian travel agent to obtain a letter of invitation.
US male citizens need to fill out a form to promise not to spy (although they don't check if you cross your fingers) and French citizens need to provide 3 months bank statements.
As it's more convoluted than most we recommend using a visa agency, but the steps to do it yourself can be found here: http://www.waytorussia.net/RussianVisa/ almost 7 years ago
Yes but you need a visa obtained in advance
Invitation letter isn't difficult and can be provided by a hotel if you don't want go through an agent.
If you are not staying in a hotel, then you will need a private invitation (Izvisheniye) - much more difficult to obtain.
Lots more up to date and official info here
http://travel.state.gov/travel/cis_pa_tw/cis/cis_1006.html almost 7 years ago