Исправления, отмеченные в комментариях.
def Quicksort1(array, low, high): #fix
if high > low:
index = Partition(array, low, high) #fix
Quicksort1(array, low, index - 1) #fix
Quicksort1(array, index + 1, high) #fix
def Partition(array, low, high): #fix
firstitem = array[low]
j = low
for i in range(low+1, high+1): #fix
if array[i] < firstitem:
j+=1
array[j], array[i] = array[i], array[j]
index = j
array[low], array[index] = array[index], array[low]
return index #fix
array = [10, 3, 4, 8, 1, 7]
Quicksort1(array, 0, len(array)-1) #fix
for j in range(len(array)): #fix
print ("%d" %array[j]) #fix