Latin Quarter Hotel

You could try Hotel Fontaines du Luxembourg.
It's a block or two east of the northeast corner of the Luxembourg Gardens, I guess you would call that the southern part of the Latin Quarter.

You mentioned free breakfast, most hotels in Paris charge (a lot) for breakfast. Also, in general, (yes, there are exceptions) Paris breakfasts tend to not be what we would think of as breakfast.

Hôtel Clément 6, rue Clément, 75006 Paris
http://www.hotelclementparis.com/en/

Pas de Calais 59 rue des Saints Pères , 75006 Paris
http://www.hotelpasdecalais.com/en/accueil

A little further away but cheaper.
ibis Paris Alésia Montparnasse 14ème 49, rue des Plantes, 75014 PARIS
http://www.accorhotels.com/en/hotel-0959-ibis-paris-alesia-montparnasse-14th/index.shtml#

I stayed at a Mercure in Paris and they had a hearty breakfast. If I were traveling with teens I would make sure there was plenty of food in the morning. This one did cater to some groups, so they had all of the usual French and American breakfast foods. Teens can eat up lots of $$$ really quickly.

We stayed at the Hotel des Nations on Rue Monge, had two adjoining rooms for wife and I and our two teen children. Had a great breakfast that was included. From balcony you could see the East end of Notre Dame and we were a block from the ancient Roman Arena and a block from the Rue Monge Metro stop. 2-3 stars, very affordable. And yes, we would stay there again.
http://www.paris-hotel-des-nations-st-germain.com/en/home/

That's funny. Breakfast is "included" not free

We enjoyed the Hotel des Grandes Ecoles on rue Cardinal Lemoine, near the Place Contrescarpe, the Mouffetard street market, and two metro stops. Breakfast was not free and a better breakfast deal was at the nearby Café Descartes (yes, that Descartes, who used to live on that block). Free breakfast is rare if not unknown in Paris hotels.

Have a look at these 3 star hotels in the Sorbonne/Luxembourg/St Germain area
http://www.hotelsaintpaulparis.com/
http://www.residencehenri4.com/en/
http://www.observatoirehotel.com/
http://www.hotelatmospheres.com/
For me I would always want to stay within walking distance of Notre Dame - the heart of old Paris.

Be aware most hotels do not include breakfast.. it is offered for an extra fee. Be careful how you read the websites .
The rates for hotels that "include breakfast" are often higher too.. plus. .breakfast is usually a cold buffet , yogurts, cheeses, deli meats, cereal, milk, juices , breads /pastries, coffee , tea etc. An egg is sometimes offered for an extra small charge. So read exactly what is offered.

We normally choose a hotel that does not include a breakfast.. and go to a café or to Breakfast in American ( full cooked egg or pancake type breakfasts) for less then 10 euros,, ( continental breakfasts at cafes can go for as little as 4-7 euros) With teen boys.. if they want a cooked breakfast.. I would think about that.. ( having raised two sons who liked big breakfasts!)

Try to find an IBIS STYLES if included WiFi and breakfast are important to you. I stay at the Ibis Styles Alesia Montparnasse. It's not too terribly far from the Latin Quarter .But there are plenty of Ibis Styles around Paris. You can't swing a dead cat without hitting an Accor hotel.

I stayed at Hotel Familia last month. It feels more French than some Paris hotels. Breakfast was typical French (croissant, baguette, juice, coffee) and included. It's about a five minute walk from three metro stations, plus a couple of good bus lines. Norte Dame is about ten minutes away. Breakfast in America is just a block away!

If you have 3 teenagers, have you considered renting an apartment? Then, you can just cook your own breakfast, which would probably be cheaper in the long run.

The cheapest breakfast is the one you buy the night before at a supermarche or small grocery store. I hate paying $30 for breakfast on vacation, which is what it usually works out to for 2 adults. Just throwing money away, save it for lunch and dinner.

I sent a reservation request to the Hotel Clement on Monday. It wasn't a actual booking request, more like a expression of interest which is all their site would allow. They emailed me back and said they'd let me know, probably by Friday??? I still haven't heard back from them but, after all, it's only Thursday. Guess they have more guests than they know what to do with.

I, too, have stayed at the Hotel Familia. It was quaint but I found it to be very noisy. Also, I tried to sleep in my first day there and received two phone calls from the front desk telling me that breakfast is ready. This was before 9AM.