Irish people don't tend to use middle names, you seldom see them on baptism or birth Certs but they often acquire them when they go abroad.
The middle name they use maybe one they took for confirmation or just a family name.
You could look for Francis' marriage and baptisim.
I have a problem with the 1911 census, not the parents age, that difference is common, it's the number of children, it says 4 not 5. I count five James, Tommie, Mary Ellen (married) Lizzie (on 1901 and Mary Ellen's marriage cert) and Maggie. Hope I haven't sent you astray.
Edit I should have looked at the original 5 is crossed out, I wonder if Francis was married before and Mary Ellen isn't Mary's child, or the Enumerator interfered as only 4 of her children were there.