I have this working in advanced search :
catalogsearch/advanced/result/?name=vanille&is_bio=1
Every product whose name contains "vanille" and attribute "is_bio" set to true will appear.
Now since I need to search not just in "name" but also other fields like "brands", I have to use quick search and its "q" query (correct me if I'm wrong). But in this case attributes won't have any effect :
catalogsearch/result/?q=vanille&is_bio=1
Will show every products containing "vanille" whatever the value of "is_bio".
Is there anyway to activate params in quick search ?