Do I need a visa?

Visa is not needed to go into the EU (including Spain) if you don't stay longer than 90 days.

You'll get a visa stamp in your passport at immigration on arrival in Paris. That's your 90 day visa for Schengen countries, including Spain.

above answers correct if you are going as a tourist, not working, not volunteering, not a student, not various other things, and not planning to remain in the Schengen area longer than 90 days in any 180.

Otherwise, maybe you do.

As U.S. citizen, if you're NOT going (as Nigel said) to work, to study, etc. etc. - that is, if you're going simply as a tourist, you have the right to visit France and Spain visa-free for up to 90 days (in part because we extend the same courtesy to their similar citizens**).

Go for any other reason, or as a tourist for longer than that, and you'll need a visa from the country you're going to.

The stamp you receive in your passport upon entry in Paris is NOT a visa stamp, it is an entry stamp.

*This of course doesn't mention the nice little ESTA form and $14 that we take in advance *even from those European visa waiver country citizens who are coming to the U.S. for fewer than 90 days and in a tourist status. My Italian husband has the pleasure of applying for that every two years. So it's not exactly a fully mutual system.

You're on the right track with the advice above. See also http://www.ricksteves.com/travel-tips/trip-planning/travel-documents.