For our other readers, this is a more legible version.

use warnings;
use strict;

use File::Find;

my ($recent,$nom,$rep);
my $line;
$rep = 'D:\\';

sub plus_recent {
    return unless -f;
    return if defined $recent and $recent > (stat($_))[9];

    $recent = (stat(_))[9];
    $nom = $File::Find::name;
}

find(\&plus_recent,$rep);

print $nom;

#open (LOG,"<D:\\log.log") || die ("Erreur d'ouverture de TOTO") ;
open(LOG,"$nom") ;
my @LogFilePosition=<LOG>;
close(LOG);

foreach $line (@LogFilePosition) {
    if ($line =~ /CHAINERECHERCHEE/) {
        print "C'est démarré !!";
    }
}
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The only thing I have to add to the other advice you've gotten is that you might want to add a newline to your print there.

print $nom, "\n";
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Now that I look a little more, you might want to check that your open succeeded as you do with the one you apparently commented out. I'd write it this way:

open my $log_fh, '<', $nom
    or die "Can't read '$nom': $!";
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That way you get a clear error message if it fails.

Please read Writeup Formatting Tips - in particular, surrounding your code with <code> tags will make it dramatically more legible. In the future, you should also include your output and a better description of your problem - saying "but it does not work" is usually frowned upon since there are many ways a code can "not work".

In your code, note that the line $recent = (stat(_))[9]; is missing a sigil in front of $_ - you mean $recent = (stat($_))[9];. The big problem you are encountering is likely that you are not testing your file name in your plus_recent subroutine to see if the file is a log file - you are locating the most recent file in your entire directory tree (after the $_ fix).

Note also in your commented open line you should likely use or in place of || - see Operator Precedence and Associativity.

Update: Learned something new re: stat. Thanks Bloodnok.

The sigil isn't missing in the context of the given code snippet - ...If stat is passed the special filehandle consisting of an underline, no stat is done, but the current contents of the stat structure from the last stat, lstat, or filetest are returned. ... - from stat
A user level that continues to overstate my experience :-))