I've run a live USB session on Ubuntu 14.10 before installing it. In software & Updates -> Additional Drivers I could directly select a Broadcom proprietary driver. After a click on Apply Changes, the wifi went on. Now I've installed Ubuntu for real (updating the packages during the installation process), I can still see the Broadcom driver displayed, but selecting it fails.
I've seen in other threads that people tried some complex solutions that eventually worked (BCM4352 Wireless network card issues with lubuntu 14.04 LTS).
Before trying this, do you have any idea why something would work on a live session and not a installed system ? I really wish there was a simple solution to my problem (I'm quite new with Linux). Thanks !