We did this a few years ago when our kids were about 3 and 5... Eurostar to Paris then the sleeper train to Berlin. Left Paris around 9pm and arrived in Berlin about 7am the next day. It wasn't the most direct route by train but it really suited us and from memory, the kids were free as child fares on Deutschebahn don't start until age 6. HTH
The sleeper trains are in short supply these days alas, that does sound like a really good way to do it. There is a sleeper train from Cologne to Berlin and I've found an article saying a Russian train company was running a sleeper from Paris to Berlin in 2015, but the SNCF website doesn't seem to know about it now. Such a shame, I think sleeper trains are great.
Btw you could also ferry or Eurotunnel it and drive, OP, but I assume you would rather not do that.
I do it regularly and book with Deutsche Bahn. It is one ticket with train changes in Brusseles and Cologne. In first class it costs 130 Euro per person one way if you book in advance, children up to 15 years are free on Deutsche Bahn trains. I quite like going by train (I do not like to fly at all). It gives me time to read and my dc uses wifi