Nyorera kupfuurira kweiyi ndima - Cocu neNetherlands vaivepo paEuro 2000 mushure mekunyoreswa otomatiki semuenzi. Rutivi rweDutch, naCocu mumitambo yose, rwakakunda mitambo yose yeboka uye chikamu chekupedzisira neYugoslavia. Kunyange zvakadaro, Cocu nechikwata chake vakadzingwa zvekare pashure pokurova zvibodzwa mumasemi-fainari, panguva ino vachirwa neItaly. Netherlands neCocu vakakundikana kupinda mu2002 World Cup muboka rekukodzera nePortugal neRepublic of Ireland. Muna 2003, Cocu akagamuchira kutumira kwake kwekutanga kwenyika yose mumutambo wehushamwari neBelgium. Netherlands yakaita zvakanaka mumakwikwi eEuro 2004, naCocu achihwina kaviri (ese ari maviri mumitambo yakaparadzana neAustria). Mukati meEuro 2004
, Cocu akasarudzwa semutungamiriri wechikwata uye akaonekwa mumitambo yese. Mumakwikwi emakota ekupedzisira vachirwa neSweden, akatadza kuwana penareta, asi Netherlands yakakwanisa kukunda. Mumakwikwi ekupedzisira, chikwata chakabviswa nePortugal. Mushure meEuro 2004, Cocu akarasikirwa nebasa rekutungamira kuna Edgar Davids, sarudzo yakaitwa nemaneja mutsva Marco van Basten.