Are there major printer manufacturers in Europe?

Irrelevant. The law would mandate requirements for printers sold in the territory. If it's non-compliant, it can't legally be sold.

Doesn't matter if HP is an American company, their products would be illegal to sell in the EU. They have to produce a compliant product or just not sell anything.

I'm actually wondering the opposite.

If 90% of printers in the EU are manufactured by foreign companies that's more in line with their consumer-friendly regulations targeting US tech companies, than if there's a local printer monopoly benefiting from outrageous ink prices.

The big ones are either American or Japanese

Does that matter? I would think it's whoever wants to sell to European consumers that matters.