U qor sii socodka faqradan - Gené ma awoodin inuu helo darawal tayo leh sanadka 2001, wuxuu doortay inuu la saxiixo Williams si uu u noqdo darawal tijaabo ah. Waxa uu saddex Grand Prix u waday kooxda isagoo ah bedel ku meel gaar ah. Midka ugu horeeya wuxuu ahaa 2003 Italian Grand Prix, halkaas oo Ralf Schumacher uusan awoodin inuu tartamo sababtoo ah dhaawac maskaxeed. Gené wuxuu si fiican u beddelay saaxiibkiis, isagoo ururiyay afar dhibcood oo ah kaalinta shanaad, laakiin Schumacher wuxuu ku soo laabtay gaariga tartanka xiga ee Mareykanka. Kadib dhaawac dhabarka ah oo soo gaaray Schumacher 2004 USGP, Gené wuxuu ku dhex maray Faransiiska
iyo British Grand Prix, laakiin markii dambe wuxuu lumiyay kursiga tartanka Antônio Pizzonia mana uusan mar kale tartan ku jirin F1.