Having a pleasant dining experience in a hotel with a baby?

I have raised three children and know the problem intimately. This answer is about bringing the baby along (you asked: "is there another solution to this problem?")

At the Northern end of Rue Mouffetard, you'll find a covey of small restaurants, all of which provide a venue for comfortable, family-friendly restaurants. There's about a dozen of these within 100 meters of Place de la Contrescarpe. These are very 'local' and reasonably priced (if anything at all in Paris is reasonably priced).

Source: Google, fair use

The Mouff' is really narrow at the Northern end, if you head south on the same street, there are outside tables with the same atmosphere.

NOTE: you should try to clear out by about 20:30 because the neighbourhood can get quite "lively" after that and no place for an infant. Not dangerous mind you, just spirited (De nuit, c'est la partie la plus touristique et active).

You may find this link from ParisInfo helpful : http://en.parisinfo.com/where-to-eat-in-paris/info/guides/restaurants-with-the-family

NOTE: Hotels are all over the Mouffetard neighbourhood, especially near the south end. Having to walk 10 - 20 meters is a great proxy for a hotel lobby.

NOTE: My last time through with an infant was at the Paris Saint Cloud Hôtel near the Bois de Boulogne. Per the usual I asked and got and isolated room just for that purpose. We took breakfast at the hotel and he screamed and threw food. As did all the other children. Nobody gave it a second glance.

In general, most restaurants in Paris will accept childs/babies with no particular issues, except maybe in the expensive ones. A good way to check the restaurant acceptance is to ask for a 'siège enfant' (child seat), many restaurants have one or two ready for customers. If you intend to keep your baby in it's trolley, just be careful not to disturb other customers or waiters movements. You should look for a restaurant where tables are not too close to each other.

Most restaurants in Paris will not be open for service at 5 PM, they usually begin around 7 PM. This means you will need to look either for 'brasseries' type (the kind depicted by Gayot Fow), or all day service restaurants, which restrict your choice, especially if you're looking for typical french meal. You will find a lot of asian shops where you can get hot meals about any moment in day.Also in touristic areas, you have more chances to find an all day service place, but that might not be the best bargain ....

I will therefore suggest that you go for a nice walk around your hotel (depending on it's location) and keep your eyes open to find a place that suits your need. Having your baby with you can sometimes be an opportunity for social exchanges ('how lovely ! how old is he/she ?').

Extras : if you have a feeding bottle or some prepared food for the baby, most restaurants will happily warm it for you in their kitchen. Although public breast feeding is commonly accepted in France, it is more subtle to feel whether a given place is fitted for it.