Someone sent me a picture of this Constantine I as Caesar with CONCORDIA MILITVM reverse today and told me that the legend is FL VAL C CONSTANTINVS NOB C.
RIC does not list this obverse legend though. RIC VI Alexandria 85 has an obverse of FL VAL CONSTANTINVS NOB C; however, on this coin it is not very clear. It looks like there is enough room for the extra C; but I remain undecided.
The first picture below (with someone holding it) is the coin in question; the second example is for comparison.