This is a faq: see How do I compute the difference of two arrays? How do I compute the intersection of two arrays? in perlfaq4.

Assuming no special characters in your inputs, you could repair your code by using the special variable $" - it controls how arrays are interpolated into strings. Something like:

@array = <FILE>;
@pattern = <FILE2>;
local $" = '|';
foreach $line(@array) {
    if ($line =~ m/@pattern/) {
        print $line;
    }
}
[download]

| functions as an or in regular expressions; see Metacharacters in perlre. If your input may contain regular expression metacharacters, you can use \Q and \E with a map to escape those and accomplish the same thing (see Quote and Quote like Operators in perlop):

@array = <FILE>;
@pattern = map "\Q$_\E", <FILE2>;
local $" = '|';
foreach $line(@array) {
    if ($line =~ m/@pattern/) {
        print $line;
    }
}
[download]

Finally, please wrap code in <code> tags to preserve formatting and make downloading code easier for monk who wish to help; see Writeup Formatting Tips.