At BCN the 2 terminals are physically separate buildings, some distance apart. So it is not like FCO.
So this can work only if everything, but really everything, works out perfectly. But that rarely happens, so I would not risk it - unless you don't mind buying a new expensive ticket if you miss that flight.

But if you are a gambler, here are the data:
Getting from the plane to the front of terminal 2 takes no longer than 5-10 minutes. (Longer if you arrive from a non-Schengen country. And if bad luck assigns you a bus gate, you will probably not make it. Although even then the layout of terminal 2 means that from where the bus drops you off, you are outside the terminal in 3 minutes.) To your advantage, FR is often on time. And I estimate that only 10-20 % of my FR flights at BCN use buses.
From outside terminal 2 you need to take a bus between terminals. At that time of the day there is (officially) a bus every 4 minutes and the ride takes about 10 minutes.
I often arrive at terminal 1 for Schengen flights 40 minutes before departure without problems. But the bad thing is that for security you don't have automatic access to the priority lane with SkyPriority. You have to go to the check in desk to get a pass for that. (Security at BCN usually only takes a few minutes, so generally I don't bother.)
Once you are through security, you can make it to any gate in 5 minutes at a brisk pace. (Shops will be open, so take a shortcut through them if you have a B gate. But do NOT enter the main tax free shop in front of you after security, because it does not have an exit in the back.)