On my way to Paris, I will have an 8-hour layover in Moscow (SVO) in Russia from 5 in the morning until 1 in the afternoon.
Will I have enough time to leave the airport and spend a few hours in Moscow and still be able to get back, clear security and make my connecting flight in time, or should I just find ways to keep myself occupied at the airport?
8-hour layover is completely enough to see some sights in the center of Moscow. To avoid traffic jams just use "Aeroexpress" (airtrain). It departures every 20-30 minutes and it takes about 40 minutes to get from SVO to Belorusskaya railway and metro stations - which is not far from the center of Moscow. So, you'll have about 4-5 hours for sightseeing.
I used to travel a lot and I haven't noticed any difficulties during passport control in SVO. So, I think you have a good chance to wander in the center.