Just to clear the whole thing up a bit:
At the airport I work on FR has replaced the traditional check-in desks (except AFIAK for those for non-Schengen or non-EU flights due to the requirement of checking the visas for non-EU citizens) with checkin computer terminals.
If you chose airport checkin you'll got there with your iternerary and your credit card (which you will need for identification purposes). You'll insert your credit card and enter your details (booking number, name etc.). Then the machine will print out a boarding pass. Now, if you have hold luggage, you'll proceed to a luggage drop-off desk (one of the old checkin desks), where some airport employee will take your luggage and tag it, putting a luggage sticker on your boarding pass.
BTW, there is an internet cafe located on the balcony level of the terminal. There you can reprint your boarding pass for as little as 50 Euro cents.