My advice is do not attempt renaming but first generate a list of moves and then review that list

See similar questions Changing filenames, Multiple File Rename

So, I would start with a program like

#!/usr/bin/perl --
use strict; use warnings;
use Data::Dump qw/ dd pp /;
use File::Basename qw/ fileparse /;
use File::Copy qw/ move /; # RENAME
Main( @ARGV );
exit( 0 );
sub Main {
    my @files = qw'
    err/error.txt
GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_103
+721.jpg
GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_103
+721.xml
blah_foo.jpg
blah_bar.xml
blah/foo.jpg
blah/bar.xml
    ';

    my @rename = makeRenameList( @files );
    fakeRename( @rename );
}

sub fakeRename {
    print "\n";
    for my $name ( @_ ){
        print "rename ", pp( $name ), "\n\n";
    }
}

sub makeRenameList {
    my @fromTo;
    my %rename_index  = (
        qw/ .jpg  1 .xml 1 /
    );

LOOP_FROMFILE:
    for my $fromFile ( @_ ){
        my($directory, $filename, $suffix) =  $fromFile =~ m{^(.*?)(?:
+([^/]*?)(\.[^\.]*))?$};

        if( not exists $rename_index{lc $suffix} ){
            warn "Unknown suffix ($suffix) ignoring($fromFile)";
            next LOOP_FROMFILE;
        }

        my $toFile = join '',
                        $directory,
                        $rename_index{lc $suffix}++,
                        $suffix;
        push @fromTo, [ $fromFile, $toFile ];
    }
    return @fromTo;
}
__END__
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Which would print

Unknown suffix (.txt) ignoring(err/error.txt) at - line 41.

rename [
  "GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_
+103721.jpg",
  "1.jpg",
]

rename [
  "GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_
+103721.xml",
  "1.xml",
]

rename ["blah_foo.jpg", "2.jpg"]

rename ["blah_bar.xml", "2.xml"]

rename ["blah/foo.jpg", "blah/3.jpg"]

rename ["blah/bar.xml", "blah/3.xml"]
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Next I might change sub makeRenameList to

and so on and so forth, until I'm satisfied with output of fakeRename, than I might call realRename :)

I agree with the previous reply: your script should just print out a list of "oldname newname" pairs (one pair per line). Once you confirm that the names are coming out right, just include "mv" (or "rename", depending on your OS) at the start of each line, and you can use the list as a shell script to actually change the file names.

For that matter, it might be easier for you to create the list of original file names as a list that your script can read as input, instead of using 'glob' in the script. That way, if you still have trouble getting it to do what you want. you can post a few lines from the input list, along with the script that tries to work on that input, so we'll have a better idea of the problem.

It is not clear if the files should be renamed sequentially then moved to the new directory, or if the files should be moved then renamed.

Anyway, here is one way you might do the former... if you need the latter this can easily be adapted. This looks for all the .jpg files in the specified directory then only proceeds if there is a corresponding .xml file. The sort on @files is not strictly necessary and could be removed; glob() returns file names in OS sorting order. If you need some other order though, that is a good place to specify it.

Note: As this is written, if there are files already in one of the destination directories with the same name as the renamed jpeg/xml files, they will be clobbered.

use warnings;
use strict;
use File::Basename;
use File::Copy;

my $dir = 'ParticleAcquisitionDataImages/'; # or whatever
my @files = glob "${dir}*.jpg";

my $rename_index = 1;

for my $file ( sort @files ){
    next if -d $file;
    my($filename, $directory, $suffix) = fileparse($file, '.jpg');
    next unless -e "${dir}$filename.xml";
    $filename = changename($filename);
    open my $fh, '<', "${dir}$filename.xml" or die "$!";
    seek($fh, 498, 0);
    my $newdir;
    read($fh, $newdir, 3);
    close $fh;
    substr $newdir, 1, 1, ''; 
    mkdir "$dir$newdir" unless -e "$dir$newdir";
    for my $ext ( qw/.jpg .xml/) {
        move "$dir$filename$ext", "$dir$newdir/$filename$ext" or die $
+!;
    }
}

sub changename {
    my $filename = shift;
    for my $suffix ( qw/.jpg .xml/) {
        rename "$dir$filename$suffix", "$dir$rename_index$suffix" or d
+ie $!;
    }
    return $rename_index++;
}
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Thank you so much to everybody for the help.