Air France and KLM have Delta flights and their own SkyTeam partner airline flights from Los Angeles LAX to Madrid on sale for as low as $287.27 round trip. Ticket prices are $307 and under for departure dates from September 10 to April 22, 2020. There are many different choices for flight itineraries. I found itineraries on different dates flying Air France, Alitalia, Delta and KLM with different possibilities for connecting cities.
KLM Los Angeles LAX – New York JFK – Madrid MAD – New York JFK – LAX
Air France Los Angeles LAX – Paris CDG – Madrid MAD – Paris CDG – LAX
Air France is a little more expensive to fly in both directions, but I prefer the idea of being stuck in Paris if there is a flight problem rather than spending time in New York for flight delays.