The drive from CDG T2
is quoted as 80 km / 1h 03 min by Google Maps.
However you will need to factor in that deplaning takes some time, rushing through the terminal, passport control.
I used taxi from CDG
T1 to Suresnes (and back) a couple of times a few years ago, which is a 34 km drive to west of Bois de Bologne.
IIRC, fare was around the 40-45 € mark (IIRC largely based on distance, not travel time which was up to 1 hour).
So, a 80 km drive to BVA
should set you back by around (very roughly) 100 EUR.
As you only have 2h20 to make the connection, I would not risk it.
For me 2h20 is just enough time to make a connection within CDG T2
- or between T2
and T1, but nothing more.
Carpe diem ! Life is too short to waste your time ! Keep in mind, that today is the first day of the rest of your life !