  We use the critical point large $N$ formalism to calculate the critical
exponents corresponding to the fermion mass operator and flavour non-singlet
fermion bilinear operator in the universality class of Quantum Electrodynamics
(QED) coupled to the Gross-Neveu model for an $SU(N)$ flavour symmetry in
$d$-dimensions. The $\epsilon$ expansion of the exponents in $d$ $=$ $4$ $-$
$2\epsilon$ dimensions are in agreement with recent three and four loop
perturbative evaluations of both renormalization group functions of these
operators. Estimates of the value of the non-singlet operator exponent in three
dimensions are provided.
