Following a “BLEEDS OFF” take-off (See 188.8.131.52) from Runway (RWY) 25 at Reus Airport (LERS), Spain, the aircraft climbed to its cruising level of FL320 enroute to Dublin Airport (EIDW). Shortly after becoming established in the cruise, the “Cabin Altitude (CAB ALT)” horn sounded. Unable to control the cabin altitude rising further the Captain initiated an emergency descent. During this descent, the flight crew discovered that the engine bleed switches were selected in the “OFF” position. The aircraft diverted to Biarritz (LFBZ), in France, where it landed without further incident.