my @lines = <$fh>;                  # read whole file

foreach (0 .. $#lines)
{
    if ($lines[$_] =~ /$regex/)
    {
        printf "Match found on line %d\n", ($_ + 1);
        $match = 1;
    }
}
[download]

No need to read the whole file at once:

while ( <$fh> )
{
    if ( /$regex/ )
    {
        print "Match found on line $.\n";
        $match = 1;
    }
}
[download]

This may solve your multi-line problem (UNTESTED):

my $lines;
while ( <$fh> )
{
    $lines .= $_;
    if ( $lines =~ /($regex)/sm )
    {
        my $newlines = $1 =~ tr/\n//;
        if ( $newlines )
        {
            print "Match found on lines ", $. - $newlines, " through $
+.\n";
        }
        else
        {
            print "Match found on line $.\n";
        }
        $match = 1;
        $lines = $_;
    }
}
[download]