Air France, Delta, Virgin Atlantic have several destinations with low summer fares from San Francisco June to August. Delta tickets in mid-August price at $444 on its website for SFO to Stockholm. Gothenburg, Sweden is similarly priced and tickets to Copenhagen are in low $500s.
Ticket prices may be lower through online travel agencies found in Momondo.com or Skyscanner.com searches.
There are also good deals SFO to Manchester UK for summer travel with Virgin Atlantic and Delta.
Delta Airlines San Francisco SFO (AF) – Paris CDG (AF) – Stockholm ARN (DL) – New York JFK (DL) – SFO
Delta Airlines San Francisco SFO (AF) – Paris CDG (AF) – Copenhagen (AF) – New York JFK (DL) – SFO
Momondo.com search for July 4-12 turned up Air France/KLM/Delta flights for $484 round trip.
Citiair.com ticket San Francisco – Paris CDG – Stockholm ARN (Air France) – Amsterdam (KLM) – Detroit DTW – SFO (Delta)
$488.46 round trip Tue July 4 – Wed July 12 was price on Citiair.com.