As a tourist travelling from Moscow to Paris, how much cash would I have to show that I have enough prior to taking the flight?
Prior to taking the flight? Usually none -- though the airline usually wants to be paid for your ticket in advance, but that doesn't usually happen using cash.
At arrival in Paris, if you're bringing cash (in any currency) totalling more than 10,000 euros in value, then you're required to declare the money at customs. This is a money-laundering regulation. The Russian authorities may have a similar reporting requirement at the departure end.
Tourists are also supposed to be able to demonstrate at the immigration control that they have the means to support themselves during their trip and leave the Schengen area afterwards. But this does not have to be in the form of cash; a return ticket and credit card (possibly with bank statements) will usually be accepted. There is also not any fixed amount of money that will be asked for -- how much it will cost to maintain yourself will naturally depend completely on how long your trip is.
At http://ec.europa.eu/dgs/home-affairs/e-library/documents/policies/borders-and-visas/schengen/docs/handbook-annex_25_en.pdf one finds a guideline value of 120 euros per day of the trip if you don't have pre-paid accommodation. This value is for visa applications, but it is probably as good a rule of thumb as we'll get for how much you need to have available to you to pass the border interview easily. Lower amounts will not lead to an automatic refusal of entry, but you may need to explain in more detail how the funds you have will be enough to maintain yourself for the trip.