Sorting by the length starting from the longest is a common way. Instead of looping over the dictionary, you can build a regex from all the terms, and return the translation based on the matching part. Also, storing the dictionary in a hash makes retrieving the translation easier and faster. Something like the following:

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

use utf8;
use open 'OUT', ':encoding(UTF-8)', ':std';

my %dictionary = (
 'animal source food'   => 'aliment d’origine animale',
 'balanced diet'        => 'régime alimentaire équilibré',
 'food'                 => 'aliment',
 'nutrition'            => 'nutrition',
 'nutrition assessment' => 'évaluation de l’état nutritionnel'
);

my $text = 'nutrition and animal source food or nutrition assessment';

my $regex = join '|',
            map quotemeta,
            sort { length $b <=> length $a }
            keys %dictionary;

while ($text =~ /($regex)/g) {
    say $dictionary{$1};
}
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Output:

nutrition
aliment d’origine animale
évaluation de l’état nutritionnel
[download]