According to Jungian psychology and to many folklorists, 'archetypes' are common and universal motifs, found in human cultures, literature, folklore etc.
'Beauty and the Beast' also contains several archetypes, some comple and some simple and primordial. Of these, the most basic ones are the following
1. Nobleman/Prince turned into a Beast by magic and only to be 'rescued' or restored to original state by the love of a good/true woman
2. Poor but purehearted and lovely young Maiden, finds true love by 'taming' a wild and savage Beast who then turns out to be a prince or nobleman.
As you can see, there are symbolic elements herein, which refere to character and other such 'universal' aspects of human personalities and lives.
Im sure that with a proper detailed study of the story and some research, you can come up with a number of other archetypes too! good luck.
I agree with iklan, however I also think that archetypes are dependant on the context in which you read (or view) something. For example, a feminist reading of the beauty and the beast reveals the stereotypical female, opressed by a male dominant society (shown in her father and Gaston) who is entrapped in a castle until she falls in love with the beast. Obviously this can be taken to ridiculous lengths but I do think it's important to consider which reading the archetype is relevant to.