As igelkott says a HoA is the way to go. It looks as though monkey is the record separator. Setting Perl's record separator might help.

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;
$Data::Dumper::Indent = 1;

$/ = q{monkey};
my %hash;
while (<DATA>){
  my ($country, $fox_hour) = /forest\s+(\w+).*-fox\s+(\d{4})/s;
  next unless $country;
  push @{$hash{$country}}, $fox_hour;
}

print Dumper \%hash;

__DATA__
forest France
-wolf
-toad
-fox 1350

monkey

land
-dog
-cat
-slug

forest France
-deer
-swan
-fox 1426

monkey

forest USA
-deer
-swan
-fox 1560

monkey
[download]

outputs

$VAR1 = {
  'France' => [
    '1350',
    '1426'
  ],
  'USA' => [
    '1560'
  ]
};
[download]

update: added link