It would be better to minimise the change to the global $/ (record separator) variable, as this may cause action at a distance in some other part of the code (or a module). This is done by reducing the scope to the shortest possible block.

You are also repeating yourself. This is not good.

my $string = slurp($file1) . slurp($file2);

sub slurp {
    my $file = shift;
    open $fh, <, $file or do {
        warn "Failed to open $file for input: $!\n";
        return '';
    }

    local $/ = undef;
    return <$fh>;
    # $fh goes out of scope, file closed automatically
}
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