Affordable lodging in Paris... with a balcony

I'm afraid you're going to have to define your per-night budget for affordable before we can offer any suggestions,

That is what sidewalk cafes are for. Finding any hotel with a usable balcony will be difficult and impossible if you use the phrase -- affordable -- Of course anything is affordable if you have enough afford. You can find French balconies which are really floor length windows/doors that will open to a iron railing but not a true balcony that you can sit on.

By affordable, I'd say under $200 per night. Wishful thinking?

You don't mention hotel vs apartment, but VRBO has an "outdoor space" filter, while AirBnB does not.

And remember, when renting apartments through agencies for Paris, such as AirBnB, you must verify that the place is legally registered to operate, with a reg. number; or you could be out of luck when you arrive if they suddenly are shut down.
There are hotel/apartments which you can search for, which nowadays are a safer prospect.
Lots of info on this forum if you search back.
Let us know what you find!

With an actual-actual balcony, good luck. Maybe a Juliette balcony.

Also consider that most Paris hotels are converted from something else, so every room is different. Any given hotel may have one or several or no rooms with "balconies" each of which is different. Also something to keep in mind when booking your room, there's really no telling what you will get until you check in and see the room.

Alas, very wishful thinking.

As noted, in Paris, that is what cafes are for. There’s no time restrictions on patio tables nor are there for park benches.

Room balconies are not the norm is the older buildings which is what you will find in Paris.

Hotel De Sers has a suite costing near $500 a night with a balcony.

I stayed at the Hotel Legend in the St Germain neighborhood that had a small balcony--big enough for a chair, perhaps 2--overlooking the Rue de Rennes with an endlessly fascinating view of the comings and goings of a gorgeous old apartment building across the street. This was 6 years ago and the cost was around $200 US then, no idea now but you might look into it.

Hotel College de France has some rooms with balconies. You may even be able to find one for under $200 per night, assuming the $ is USD. A few years ago I missed my train and stayed at Le Grey Hotel and had a room with a usable balcony. It cost less than $200 per night but that was a same day booking made in August. You'll need to check the price,