Passport

No, once it is issued, it is valid until its' expiration date. You don't have to wait to use it.

The issue is not how new it is but how much time is left on it. It is a bit risky to have a passport that expire in less than 6 mos after date of entry for Schengen, but no risk of a newly issued passport.

For the Schengen region passports need three months validity.

Your passport must be valid for a minimum of six months at entry, and valid for an additional three months beyond your planned date of departure from the Schengen area.

From the French Consulate website Washington DC:
"... Your passport must be valid for at least 90 days after your date of return from the Schengen zone..."
http://tinyurl.com/o6ac3vx

When you enter Schengen you have 90 days of visa so to have 90 days after possible date of departure you need 6 months. If your ticket says you are returning in one month then of course 4 months should do it -- but it depends on how the airline or the immigration official interprets it. Airlines occasionally won't let people board without 6 mos.

Some of these responses baffle me, as your passport is new and not expiring.

The answer is no. You are good to go. Happy travels!

Thank you April. I too am baffled by most of the responses. The OP didn't ask about expiration dates at all.