You can create a dict and pass this as the data param to the dataframe constructor:
In [235]:
df = pd.DataFrame({'Gene':s.index, 'count':s.values})
df
Out[235]:
Gene count
0 Ezh2 2
1 Hmgb 7
2 Irf1 1
Alternatively you can create a df from the series, you need to call reset_index
as the index will be used and then rename the columns:
In [237]:
df = pd.DataFrame(s).reset_index()
df.columns = ['Gene', 'count']
df
Out[237]:
Gene count
0 Ezh2 2
1 Hmgb 7
2 Irf1 1