moving around paris with a family of 9

How old are all these people? Do any of them have any mobility issues that would slow them down? Would you consider breaking into smaller groups to explore according to people's individual interests? You should look into booking small private group tours at some attractions. I think the threshold is probably 10 people but you could probably work something out.

Scheduled Metro departure??? There are no scheduled metro departures. You research which line you need to travel and which direction. You descend into the metro and follow the correct signs. When you arrive at the platform you wait for the next metro to arrive. It's also important to know "how many stops" until you arrive at the stop you want.

We usually take groups around 20 with 4 adults and the rest are 15 years old. It's really not that difficult.

You can use Google Maps to get estimated travel time (on foot or using public transportation) between points of interest or addresses. I've never paid much attention to the public-transit estimates, but the walking times seem quite reasonable, assuming you don't have mobility impairments to worry about. And, obviously, assuming people don't get distracted by the architecture, the shop windows, the markets, etc., along the way.

The Metros are usually running every 5 minutes or so. You just arrive at the platform and wait for the next one. There will be an overhead digital timer to tell you how many minutes before the next one arrives.

To give you a very general idea, if I was going from the Latin Quarter to the Eiffel Tower, it would probably take 20 minutes from time of stepping out of the hotel to riding on the Metro to standing underneath the Eiffel Tower if I had a few slower people walking with me.

Everyone in your group needs to know the 'missed metro rule' if you are going to move together as a group. i.e. if part of the group gets on the metro and someone gets left behind, the first group gets off at the next stop and waits on the platform. The left behinds get on the next train and go one stop and rejoin the group on the platform. You will be glad everyone knows this if it happens and with a group of 9 it is not unlikely especially at busy periods.

Also be sure everyone in the group has a card for the hotel with hotel address so they can find their way back if they get separated.

I would be breaking this group up several times in the time in Paris. Plan some days where groups head in different directions depending on interest and then meet up for dinner. e.g. I can't imagine that in a group this size there are not some people who want to shop and some people for whom this is hell on earth -- so do different things. The same may be true for particular visits e.g. some may long to see the catacombs or tour the sewers and others, just not want to do that. We break up even in our family of 4 or 5 on occasion when we travel together. It does keep people happier with each other than being dragged along to things they don't want to do or when they really long to sit and sip at a cafe or read a book in the park.

You can use the Paris Transportation site to determine routes and transit times.

For your own sanity, break up the groups if you can. Paris is a busy place and to try and always keep track of 9 people would be a nightmare. Metros are continuously running but give yourself lots of time to get places. More so based on extensive security checks everywhere you go