passport

There is no such thing as a "European passport".

Eventually, when a series of conditions is met, someone could get a French passport, or an Italian one, or a Swedish one, etc.

Not easy though.

But you dont need a passport of a European country to work there. You need a residency permit and a work permit. If you have those two, you can work and stay in the country on your American (or whatever) passport.

Work and residency permits are not easy to get either though. The rules differ greatly from country to country - so decide on what country or countries you'd be willing to go to first, then look up the info by country.