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We study the average error term in the usual approximation to the number of$y$-friable integers congruent to $a$ modulo $q$, where $a\neq 0$ is a fixedinteger. We show that in the range $\exp\{(\log\log x)^{5/3+\varepsilon}\} \leqy \leq x$ and on average over $q\leq x/M$ with $M\rightarrow \infty$ ofmoderate size, this average error term is asymptotic to $-|a|\Psi(x/|a|,y)/2x$.Previous results of this sort were obtained by the second author for reasonablydense sequences, however the sequence of $y$-friable integers studied in thecurrent paper is thin, and required the use of different techniques, which arespecific to friable integers.

Entiers friables dans des progressions arithm\'etiques de grand module