Take a peek at this relevant question. You can make your index a column in the pandas dataframe for output.
Right before your output within your python script @pscript you can add: df.reset_index(inplace=True). 
Then in your WITH RESULT SETS statement you can add the index column first in the list:
WITH RESULT SETS(
(
 MyIndex int,
 Col1 FLOAT,
 Col2 FLOAT, 
 Col3 FLOAT 
));
Here is a full simplified example since I can't see your exact code:
EXEC sp_execute_external_script  @language =N'Python',
@script=N'
import pandas as pd
s = pd.Series([5,6,7,8,9,10])
df = pd.DataFrame(s)
df.reset_index(inplace=True)
OutputDataSet = df
'
WITH RESULT SETS (( MyIndex int, test int ));