- how early should we arrive at the station - getting dropped off by taxi?
- what happens if we miss our train is our ticket good for the next train?
Paris - Metz train departs from Gare de l'Est.
Fully flexible tickets (the most expensive at around 84€) allows you to take trains up two hours after your ticketed / scheduled departure time, without fees.
If you arrive 40 minutes before your departure, you should have plenty of time to purchase tickets and find the train platform before departure. You could reduce this time greatly (say to 20 minutes before departure) by having your tickets purchased before you arrive (can do so at any of the major train stations in Paris or online and have a mobile phone ticket available for scanning).