my ( $week, $comptage, $index ) = qw{ W C I };
my $cmdc2= qq{mv M3.*txt ../../../dir_first_action_${week}/dir_M3_${we
+ek}_comptage_${comptage}_${index}};
print $cmdc2;
#Output:
#mv M3.*txt ../../../dir_first_action_W/dir_M3_W_comptage_C_I
[download]

How does it "not work"?

Are you expecting the unix command mv to run? If so, you need to use qx{} or backticks, not qq{}. See Quote Like Operators in perlop.

Update: Forgot to mention backticks