This is an example of the "animal groom" tale, known in many variants from around the world.  The first known literary version was by Mme. de Villeneuve and ran to 362 pages!  Most subsequent versions are based on Madame Le Prince de Beaumont's version, which we are reading.  A variety of literary retellings and reprintings in 19th century "imprinted [the tale] on the cultural subconscious of French, English, and Americans" (Hearne 2).  There have also been many further versions in the 20th century, including film and opera.
        In this story, in contrast to many female-centered fairy tales, the heroine is active and the hero must take a passive, waiting role.  It is for Beauty to make decisions and to act on them (she decides to return with her father, even though she thinks she will die; she chooses to return to Beast and to accept his proposal; although she is technically his prisoner, he does not force himself on her but awaits her positive decision to accept him).
        Even more than "Cinderella," this is a story about appearances and how they can deceive.  Beauty must recognize the inner virtue of the beast before he can be transformed.  It is also to some extent about the mutual education that must take place, as Beast learns to modify his anger and violence (in the original story expressed only against her father, not against Beauty) and Beauty must learn to look beneath the surface.  I would maintain (have, in fact, in my dissertation) that this element of education is what separates "B&B" from other fairy tales - here, at least, there is a sense of romantic love and of motivation.
         One suggested reading (Hearne, 126 et.seq.): Beauty has a fully developed soul (psyche - cf. Cupid and Psyche) and is educated, but must explore her animal nature; she must accept this inner nature before she can love.  The rose that she requests is a symbol of love; note that Beast is willing to part with merely material possessions, but becomes enraged at theft of the rose, an emblem of suffering, love, and redemption.  The Beast himself represents that animal nature (note the correspondence between the poles in the fairy tale and the common American tale, with woman as the civilizer of the untamed male).
        Here is an extended psychological interpretation from Bruno Bettelheim:

    Beauty has an Oedipal love for her father, which must be broken for her to become fulfilled as an adult human being.  This is the story of a transference of love from the inappropriate father to a more appropriate mate, and also about the child’s fear of sexuality.  The father’s theft of the rose symbolizes his particular love for his youngest daughter, and anticipates her eventual sexual maturity, since the broken flower is a symbol for the loss of virginity (“deflowering”).  The beast of sexuality which appears at the moment of the theft represents the anxieties both the loving parent and the child feel about the onset of adult sexuality.  (Note that the Disney version, while altering much else, retains the oedipal attachment of the daughter to her father.)
    However, the Beast’s threat proves to be illusory; rather than a ferocious, destructive creature, he is a loving and tender mate.  But she does not immediately realize this.  She remains torn between her father and the Beast, wishing to return to her father’s side (many versions include a magic mirror through which she witnesses her father’s distress); only when she is removed from the Beast’s presence and realizes his suffering does she recognize where her appropriate love lies.  She must return to her father’s house to resolve her oedipal ties to her father before sex, previously repugnant, can become beautiful.
    Bettelheim tells us that many fairy tales deal with this oedipal struggle; however, “Beauty and the Beast” is unusual in that it represents the oedipal attachment as normal, positive, capable of coexisting with the love of the spouse - note the difference between this and some of the Cinderella versions.  In Joanna Cole’s version, the father tells her directly (p. 21) that she ought to marry the Beast as he desires.
    We also note here, as in many other folkloric images, the association of sexuality with the bestial.  Bettelheim notes that in many European versions of this story, the “bestial” form is that of a snake - a phallic creature.The story works off of human duality as animal and mind (especially noted in the story’s ancestor, Cupid and Psyche); the marriage of Beauty and Beast is a symbol of the control of the id (animal, sexual passions) by the superego (socially constrained intellect).

• In Andrew Lang's Blue Fairy Book, he is a kind of cross between an elephant and a wild boar.
• Several versions use a bear or a lion.
• In Jean Cocteau's 1946 film, he seems to be a lion.
• Walter Crane's famous illustration shows a creature most like a boar standing on two legs and wearing clothes.
• Boyle's version (1875) looks like a walrus.
• The illustration to Jessie Willcox Smith's Edwardian version seems to trivialize creature, who now looks like a monkey and is significantly smaller than Beauty.
• A 1982 illustration to Angela Carter's version has a one-eyed blue monster - abstract, not any real animal.

See also variants:

• East of the Sun and West of the Moon