A typical breakfast in Paris is one or two croissants (buttery rolls of flaky pastry) or a tartine (French bread sliced lengthwise, with butter and jam), some fruit or juice, and café au lait (coffee with milk, also called café crème).
The traditional spot for breakfast in Paris is a sidewalk café, unless breakfast is included in the price of your hotel room.
The pleasure of breakfasting in a Paris café is one of the reasons you've taken a trip to Paris.
Another possibility is to breakfast in a bakery. Some have a few small tables, and serve coffee (or you can bring your own), and the cost for breakfast will be lower than in a café because there are no sidewalk tables and the ambiance is different.
To save money, on some days you may want to breakfast on a bench overlooking the Seine, or in a local park. Buy your croissants from a bakery and your coffee à porter (to take away) to save money. What could be better?
Larger breakfasts are available—omelettes spring to mind—and some Paris cafés even offer mid-morning brunch.
If you are staying in an apartment, you can have whatever you like for breakfast, and save money doing it.