Upvote:7
Russia have contracted out their visa processing to VFS, go to their 'ALL ABOUT YOUR VISAS' page for more info.
Your single entry visa will be used and no longer valid when you exit Russia on the 16th. Therefore your question is really 'do I need a visa to change flights in Moscow' and the answer is (probably) no, with some conditions:
A Transit Visa is not required if you remain in the transit zone of the airport in order to catch an onward or connecting flight within 24 hours of arrival. Transit visas are normally valid for maximum of 3 days if travelling by air and 10 if travelling by train.
Assuming your Mumbai flight is within 24 hours you'll be fine -- here's more about transit from the Moscow Airport page. Which also says you'll be able to pick up a transit visa in the airport if you really need to (although it advises you not to).
Having said that Ukraine Airline will check your Russian visa when you check-in in Paris, so you're going to need proof of your outbound flight then.