You are having issues with scope. By using my to declare @array, you are essentially making it invisible outside the package. Rather, the code you've posted works as expected (I think) if you simply change that declaration to our:

my $file = "qwerty.txt";
open FILE, "< $file";
our @array = <FILE>;
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See perlmod and perlsub for information on how scoping works.

On a side note, there are a few things you are doing (an untested 2-argument open, @EXPORT instead of @EXPORT_OK, a bareword filehandle...) that I would consider poor form. I'll assume that's only because you are trying to make a demo script.