Once I buy a Paris Visite Pass, how long do I have to start using it?

Paris Visite Pass validity period doesn't start until first used and there's no expiry set for the ticket until / before that first use.  So you can buy Paris Visite pass and then not use it until tomorrow or the next day, next week, next year, etc.
 
Once the Paris Visite ticket is used for the first time, that day at midnight, the ticket will used it's first full day of validity.  For example, if you use a new/unused Paris Visite ticket in a turnstile at 11:45 p.m., the ticket will have used an entire day of validity at midnight.