San Francisco to Rome ticket prices in low $300s with SkyTeam Alliance airlines provide an opportunity for cheap travel from January to May 2020. Air France, KLM and Delta Airlines mix and match flights for a variety of airport connection itineraries. Lowest ticket prices look to be Delta operated flights via JFK. For about $15 more round trip there are all Air France and KLM flights.
My preference is to fly international flights direct from Paris or Amsterdam to SFO to avoid the time uncertainty for passing through passport control and customs in ATL or JFK before a flight connection to return to San Francisco.
Air France ticket for Delta operated flights
San Francisco SFO – New York JFK – Rome FCO – New York JFK – SFO
Air France ticket for Air France operated flights
San Francisco SFO – Paris CDG – Rome FCO – Paris CDG – SFO