The lack of any filesystem interaction notwithstanding, your mistake is in comparing 2 regexen rather than matching a string. Here's an amended version of your script showing the match actually happening.

#!/usr/bin/env perl 

use strict;
use warnings;
use diagnostics;

my $regex = qr/carlos\.txt/;
my $file  = 'juan_carlos.txt';

if (defined ($file) && ($file =~ $regex)) {
    print "File $file matched\n";
} else {
    print "File $file not matched\n";
}
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I've named the variables appropriately. Note that there's nothing in this script to say that $file is anything to do with the filesystem (yet) - the variable just has a semantic name.