Can anyone tell me what taxes and fees we would pay for a hotel vs airBnB in Lyon?
Making bookings should disclose the full price prior to the confirmation stage.
let me google that for you:
https://en.lyon-france.com/who-we-are/city-tax-lyon
In Europe all taxes are rolled into a retail price. What you see on the price tag is what you pay.
Many cities have a small per night charge for tourists, usually collected separately, and many use some of that money for such things as free bus, tram or train tickets for guests, or reduced admission to some local attractions. That should be the same regardless of accommodation type, although there are some modifications based on number of rooms in some places.
Now that's the general principle. The link provided above gives the specifics for Lyon.
You ask about fees - if you are new to airbnb you may be shocked at the number of fees airbnb adds on. Read the information on the website listing VERY carefully. If you are a regular airbnb user this won't come as a surprise.