Rec for family friendly and very nice but affordable restaurant near Eiffel Tower area

"We need to be finished eating by 6:00 pm"".

I doubt you will find a "very nice" restaurant anywhere Paris open for dinner at 5:00 pm. Even where I live, if you must eat at 5:00 the fast food places will welcome you.

Best you should get you and the kids on Paris mealtime. Bistro's and some brasseries serve all day, but an early dinner is around 7:30 PM. Consider a late light lunch after your Eiffel Tower visit, dinner after your bike tour.

Thank you for the suggestions. Unfortunately our bike tour is from 6:30 - 11 pm (a Seine river cruise from 10-11 included). So we will not have time to catch a nice dinner after the bike tour. Only option i gues is a late lunch, do restaurants remain open for lunch late around 4 and 5 pm? Any recommendations for places for a nice late lunch around the Eiffel Tower?

I love to eat at Chinese places in the afternoon when I am in Paris. There are lots of good ones in the Eiffel Tower area. They operate like delis. Cooked food is kept in cold cases and warmed by microwave after it is purchased if it is to be consumed at tables there. Much of their business is take-out. I have found good quality food consistently. For 10-15 Eu per person you can eat like kings. The kids may have fun picking out what they want to eat, since it is all on display under glass. Desserts are usually available.

You could wander over to Rue Cler. We've had decent food at Le Petit Cler.

Hundreds of cafés in that area and all over Paris where you can eat meals anytime. We mostly always eat at cafés rather than bistros and restaurants. Save a nice restaurant for the next night.
Generally you'll find on café menus: hamburgers, fries, omelettes, quiche, sandwiches, pasta, soup, salads and more. All menus are posted outside, just find one you like.

To expand on what's been said so far, most formal luncheons will not seat you after 2pm and most formal dinners will not seat you before 7pm, exceptions allowed for spots that cater to tourists, which might open doors at 6pm but no one will be there yet.
Therefore, don't plan on either a luncheon or a dinner, plan on a cafe or bistro that has light fare throughout the afternoon. Maybe even a bakery that has sandwiches.

That's not the main worrisome item in your post, though. You are scheduling yourselves for a very long day if you will be landing at the airport that morning after flying from North America with kids. And your 12:30 time at the Eiffel Tower doesn't allow, I'm guessing, for a delay in flight arrival or trouble getting to your lodging or trouble getting a room key early. That's a lot of ifs.

Merci everyone, great suggestions.
@ Avirosemail: actually we arrive very late via Eurostar the previous night and won't be at our hotel till about 12 am. Our first full day in Paris is the day of the Eiffel Tower visit.

The fad for brunch is spreading everywhere these days, including France,
so you might consider looking for a big brunch before the Eiffel Tower visit
and then living on snacks until after the tour, then go for a late dinner/snack.

May not be what you're looking for, but I like this place in the 7th. I think one of their storefronts is open continuous hours. As it says, they are more rustic and small than "nice." But it's still nice as in good quality.

https://bonjourparis.com/food-and-drink/gusto-italia-casual-italian-restaurants-paris-7th/

You can find a Brasserie open all day, into night.

Agree with Rachel about Gusto Italia. Good pizza and salad, good service, good prices. I'd go again!