/^FOO((?!BA[RZ]$).*)/ will do what you want. Reading out loud:

m{
  ^ # start of the string
  FOO
  ( # this will become $1
    (?! # must not be
      BA[RZ]$ # BAR or BAZ followed by end-of-string
    )
    .* # now anything else (except "\n")
    # no need to "$", because ".*" will happily swallow it all
  )
}x
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Checking it out:

$ perl -MData::Dumper -le '%h = map { $_ => /^FOO((?!BA[RZ]$).*)/ ? $1
+ : q(does NOT match) } qw/FOO FOOZIM FOOBAR FOOA FOOBAZ FOOBARX/; $Da
+ta::Dumper::Terse = $Data::Dumper::Indent = 1; print Dumper \%h'
{
  'FOOBAR' => 'does NOT match',
  'FOOZIM' => 'ZIM',
  'FOOA' => 'A',
  'FOOBARX' => 'BARX',
  'FOOBAZ' => 'does NOT match',
  'FOO' => ''
}
[download]