The error refers to your use of $i++ within the pattern match. If you really want to do variable interpolation evaluate code within the pattern match, then you need to enclose it with \Q\E, like so:

 /<FN\Q$i++\E>(.+)\n/
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...do something like this:

/<FN(?{$i++})(.+)\n/
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Having said that, I sniff an XY Problem here.
I'm really not sure what the purpose of that $i++ is.
Is it some sort of counter, so that you know how many footnotes you have captured?
If that's the case, you could simply do something like this (untested):

while (<FILE>) {
    chomp;  #if necessary
    if ($_ =~ m/<FN\d+>(.+)\n/) {
        push @fnote, $1;
    }
}
my $numfootnotes = scalar @fnote;
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Hope this helps,
Darren :)