You can switch. Show the Armenian passport to Russian authorities. Show the French passport to German authorities.
To the airline, what you show might depend on how long you'll be in Moscow. If it is a short time, so that you check in once for both legs of the flight, show them the French passport, as your final destination is the EU. If they say "where is your visa for Russia?" then show them the Armenian passport.
If you will be staying in Moscow, and you will check in separately for each leg of the flight, show the Armenian passport when you check in for the first leg, and the French passport when you check in for the second leg. Again, if they look for a visa to satisfy themselves that you will be able to enter the other country on your itinerary, just show them that you also have the other passport, allowing you visa-free entry into that country.