The passport must be valid at least 6 months after the date of return for the French citizens (check with the consulate or embassy for other countries).  
If you travel with your children and they are not already registered on your passport, you should know that now children, whatever their age, must also have an individual passport. 
To gather visa, in example of France: See the Consulate. 5, Av Robert Schumann, 92200 Boulogne, 01 42 05 23 18, cost of visa: 60 euro.  
To provide: 1 photo, 1 form to fill, 1 certificate of travel, getting within 8 days. Impossible to transmit the file by mail.  
Under certain circumstances, it is also possible to obtain the visa on your arrival in Ulan-Baatar. It costs 53 dollars. We are in charge to send your passport details at least two weeks before your arrival.  
Visa partner: LISCO. 76, avenue des Champs Elysées, 75008 PARIS.  01 56 43 39 69.  www.visit-office.fr