Irule redirect to the right pool depending hostname

The HTTP::host item does not include the "; text. Try this:

when HTTP_REQUEST {
 Check requested host header (set to lowercase) 
switch [string tolower [HTTP::host]] { 

   "aaa.domain.fr" { 
      pool AAA_Pool 
   } 
   "bbb.domain.fr" { 
      pool BBB_Pool 
   } 
   default { 
      pool CCC_Pool
   } 
}