my $root = rel2abs (shift || '.');
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I wouldn't use rel2abs: if I give '.' as an argument, I expect it to be honored. Unless there were some specific option to explicitly instruct the program to do otherwise, that is.

my @extList = @ARGV;
  
@extList = ('pl', 'pm') if ! exists $extList[0];
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How 'bout

my @extList = @ARGV ? @ARGV : qw/pl pm/;
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instead?

my $lines = 0;
my $files = 0;
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No need for the initializations. Maybe you want them anyway for (your) clarity. For me,

my ($lines, $files); # is clear enough
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sub count
{
my $name = $File::Find::name;
return if -d $name;
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Maybe in this case you would prefer to use the no_chdir => 1 option to find() which seems more appropriate...

my ($ext) = $name =~ /\.([^.]*)$/;
return if ! defined $ext or ! exists $exts{$ext};
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How 'bout

return if grep $name =~ /\.\Q$_$/, @extList;
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?

return if ! open inFile, '<', $name;
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open my $in, '<', $name or  # and I don't need close()
   (warn "Ouch: $name => $!\n"), return;
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++$lines while (<inFile>);
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Hmmm, I always recommend against slurping in whole files (if unnecessary), but perhaps

$lines+=<$in>;
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...