Low fares to Europe from Bay Area California airports are abundant today. One example is San Francisco to Zurich, Switzerland ZRH for $365 to $396 round trip for travel with American Airlines and Oneworld Alliance for travel from mid-August to April 2018.
Basel Airport BSL is another airport on sale for high $300s, but watch out for London change of airport itineraries between London Heathrow LHR and London Gatwick LGW, which is a real time-waster.
SkyTeam shows similar low fares on Google Flights, however, I find them re-pricing over $1,000 on Delta. SkyTeam low fares might still be found on OTA sites in Momondo.com searches.
American Airlines ticket San Francisco SFO – New York JFK – Zurich ZRH – JFK – SFO
The itinerary above sucks for long layovers in JFK. There are much better itineraries available for a few dollars more, including British Airways direct SFO to London LHR.
American Airlines Oakland OAK – Phoenix PHX – London LHR – Basel BSL – London LHR – Phoenix PHX – Oakland OAK