I think the French pronounciation is way off on this one.
Because of the vowels at the start of "un" and "enfant", both the second "s" of "suis" and the "n" of "un" should be vocalized. Am I wrong?
Regarding the liaison for suis - The liaison is optional. Whether it's pronounced or not depends on the register: the higher the register, the more likely it is to be pronounced.
Regarding the liaison for un - I hear the liaison, do you not?
The liaison must be done by "je suis "z" un enfant! (Je suis de langue française).