hippo has answered your question. I would further recommend a prompt module such as IO::Prompt::Hooked. You can get capability similar to his without writing any code.

#!/usr/bin/perl
use strict;
use warnings;
use IO::Prompt::Hooked;
my %opts = (
    message  => 'Enter namen of input fasta file',
    default  => 'chr.fa',
    validate => sub {-e $_[0]},
    error    => 'File does not exist', 
);

open my $FILE, '<',  prompt(%opts);
open my $out, '>', 'output.txt';

...;
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If your input file used the full afta spec, I would also recommend finding a module to parse it. Your code suggests that your file uses only a small part of the spec. In that case, your approach of parsing it with regular expressions is fine. However, I do see errors in both of your regexes. $header would always be a null string. $seq would contain the entire record. (I would need a copy of your file spec in order to suggest a correction.) Your second regex does not even compile. (probably a typo in your post).