Around that North station-which sits nearly sidebyside to the east station (for the trains to Germany) are dozens, if not even 100s of HTLs. Without any indication about price, comfort etc I always tell to visit a few of the dozens of HTL-booking sites (in EUR booking.com is best known) and see what it shows-it has also dozens of special search functions. Or go from googlemaps-this will also show HTLs if selected. I is now way far too early to tell about prices etc. But be aware that this is not the very best area of P. A short easy metro ride may bring you to many more HTLs.

Several of the well-known large chains however do not choose to advertise via booking and only via their own sites. Ibis-via all.accor is very big in FR, but there are again dozens others.

As Mcadv says Accor group offers a wide range of hotels at all prices, but the area around Gare Du Nord is not particularly nice, especially with children.

I assume you have heard of the Konus card for free transport around the black forest if you stay in participating lodgings.

https://bw.tourismusnetzwerk.info/wp-content/uploads/2019/05/KONUS-Flyer-PDF-Download_GB.pdf

I’m in an Ibis next to Gare de l’Est which is ten minutes walk from Gare du Nord. Part of the Accor group. Comfortable with lots of restaurants nearby. I use Booking.com. Reviews on this site can only be made if you’ve actually stayed in the hotel and in my experience are very accurate. Read the reviews carefully to find a hotel that suits your needs.

Oh I’d just add a travel kettle is a brilliant investment as lower priced hotels often don’t offer drinks in the room. Bring your own tea or coffee and UHT milk pouches and a collapsible cup 

I would try airbnb. We are using one that is close to Eifel tower and metro station… and close to the river so you are going to see lots of things on foot. Kids will have more room than a hotel