Sites to see from Paris to Reims and then Germany?

Just musing-
You have a rental car that holds seven people and their luggage?
You are taking a rental car across borders, so make sure your rental agreement covers that. What city are you flying out of? Are you returning the rental car to the same country? Dropping a rental off in a second country is very expensive. Have you checked if any of your countries require vignettes?
Safe travels with your family!

The A4 to Metz then north to Luxembourg and Trier is the way to go, in my opinion.

The top WWI sight on the way is Verdun. The memorials are well-designed, and you can see some remains of trenches, forts, etc.
There's also an American WWI memorial in Château-Thierry closer to Paris: I have not been there.

Reims itself could be worth a stop for the cathedral, but stopping in a city the size of Reims is always quite time-consuming, so I am not sure it makes sense. You can play it by ear. It depends on how many cathedrals you have seen before (personally, I've seen more than my fair share, so I might be biased).

Trier is definitely worth exploring and that is perhaps where I would stay the night.
Drive from Paris, visit Verdun on the way, sleep in Trier. Spend morning in Trier, then drive to Bacharach.

Importantly, this is all assuming that you are not planning to drive this far after a long flight from overseas! It would be dangerous to do so; Reims is as far as it'd be safe(ish) to drive.
If that was the case... Take the train from CDG to Brussels, then Brussels to Köln, sleep there, and rent a car in Köln the next day.

EDIT: I missed the bit about the 5 kids. Rent a 9-seater van, anything smaller will not have luggage space for 7. Luggage is typically not hidden from sight in such a van. I am not sure how much of a concern luggage theft can be in Verdun (it's more of a southern France thing afaik) - I do not think it is a high risk, but it is worth having in mind, so take valuables when you leave the car at least.

Thanks!

We are leasing a car. It does seat 7 but it will be tight to your point. We wanted a minivan but there weren't any available and the large travel vans (also not available) would seem like they would be impossible to park in Europe. We are travelling as light as possible with carry-on luggage only for each person.... We also lose the oldest child at the 3 week mark which will make things modestly better at that point.