alternative to lookupvalue function

My apologies. I should have looked at the structure of the map. You need to change the model slightly and consequently the measure:

Couleur Max Region New =
VAR _MXVoix =
    CALCULATE ( MAX ( 'RegNuance'[Voix] ), ALLEXCEPT ( RegNuance, Reg[Région] ) )
VAR _Colour =
    CALCULATE (
        MAX ( RegNuance[Couleur Nuance] ),
        FILTER ( ALLEXCEPT ( RegNuance, Reg[Région] ), RegNuance[Voix] = _MXVoix )
    )
RETURN
    _Colour

Sure. You need a couple of measures:

Sum Voix = 
SUM(RegNuance[Voix])

Max Voix by region = 
CALCULATE(MAX('RegNuance'[Voix]), ALLEXCEPT(RegNuance, Reg[Région]))

Filter Map by Winning Code Nuance =
VAR _ValVoix =
    SUMMARIZE ( RegNuance, Reg[Région], Nuance[Code Nuance], "@SUM", [Sum Voix] )
VAR _MAXVoix =
    ADDCOLUMNS (
        SUMMARIZE ( RegNuance, Reg[Région], Nuance[Code Nuance] ),
        "@SUM", [Max Voix by region]
    )
VAR _filter =
    CALCULATETABLE (
        VALUES ( Nuance[Code Nuance] ),
        INTERSECT ( _ValVoix, _MAXVoix )
    )
RETURN
    COUNTROWS ( _filter )

Add this last measure [Filter Map by Winning Code Nuance] to the map's filter in the filter pane and set the value to greater or equal to 1

To get:

and a bonus measure to return the winning Nuance Code by region for the maps tooltip:

Code Nuance with max votes by region =
VAR _ValVoix =
    SUMMARIZE ( RegNuance, Reg[Région], Nuance[Code Nuance], "@SUM", [Sum Voix] )
VAR _MAXVoix =
    ADDCOLUMNS (
        SUMMARIZE ( RegNuance, Reg[Région], Nuance[Code Nuance] ),
        "@SUM", [Max Voix by region]
    )
VAR _filter =
    CALCULATETABLE (
        VALUES ( Nuance[Code Nuance] ),
        INTERSECT ( _ValVoix, _MAXVoix )
    )
RETURN
    CONCATENATEX ( _filter, 'Nuance'[Code Nuance], ", " )

Hope this helps!