I wonder if in Europe they have other farm welfare benefit programs like they do in the US...

Farm subsidies can be made in the form of direct payments to the farmer or as some other economic payment: For example low interest loans that encourage farmers to expand production. Farm loan programs are a lot like student loan programs: the Government, in effect, pays a bank to give the farmer a low interest loan and then backs the loan if the student, or in this case the farmer, defaults on the loan.

Farm subsidies are a big problem on both sides of the pond.

Politicians can't resist giving the subsidies away, and then the subsidies make the original problem (usually low prices) worse than before the subsidy. The subsidy phase out period is almost always worse on the farmers than the farm "crisis" that launched the subsidy in the first place.