Your sentence is an example of what is called "redundancia pronominal" or "reduplicación/doblado de clíticos": there is an object in the canonical position ("a su novia" in your case) and also a clitic pronoun ("le" in your case) with the same syntactic function. As explained in the Enciclopedia de lingüística hispánica, by several authors, it's a phenomenon that singles out Spanish with respect to other Romance languages (but this is not exclusive of Spanish: this also happens in Catalan with a lower extent).
In your case, what is duplicated is the indirect object ("le" and "a su novia"). This book explains that there are situations in which such indirect object duplication is mandatory and others in which it is not, although the option with duplication is by far the preferred one.
The duplication is mandatory when the object (direct or indirect) in the canonical position is constructed with a pronoun (with some exceptions). For instance:
- María me llamó a mi.
- Yo le di el regalo a ella.
You cannot say "María llamó a mi" or "Yo di el regalo a ella". The exceptions to this rule are the pronouns "usted" and neutral "ello" which do not require duplication, as in these examples:
- Para servir a usted.
- Es cuanto tenemos que decir a usted, señor presidente. (CREA, España, 1996)
- La EMT agradece a usted la utilización de sus autobuses.
- Dedicaré a ello el siguiente capítulo.
In other cases, duplication of indirect object is mandatory or not depending on its semantic role: it's (relatively) optional when this object express the target or the recipient, as in this example,
- María le entregó el paquete a su dueño / María entregó el paquete a su dueño
or these other examples from the book Gramática descriptiva de la lengua española, by several authors:
- Le dijeron a Juan que viniera / Dijeron a Juan que viniera
- Le dieron el premio al escritor / Dieron el premio al escritor
But duplication is mandatory when indirect object has other semantical roles: what are called experiential ("experimentantes")
- Nunca le gustó realmente el cine a María (you cannot say "Nunca gustó realmente el cine a María"),
- María le hizo los deberes al niño (you cannot say "María hizo los deberes al niño"),
- Le preparó un brebaje al enfermo (you cannot say "Preparó un brebaje al enfermo")
and (inalienable) possessor datives
- Aquí le rompieron la pierna a Juan (you cannot say "Aquí rompieron la pierna a Juan"),
- Le cortaron las uñas al niño (you cannot say "Cortaron las uñas al niño"),
- Le duele la pierna a Pedro (you cannot say "Duele la pierna a Pedro").
Note that, in your sentence, "su novia" has the role of recipient, so it corresponds to one of the cases in which duplication is (relatively) optional: as in the example "Dieron el premio al escritor", one can also say "Miguel dio un anillo a su novia" or "Miguel dio a su novia un anillo" (which may have a slightly different nuance in meaning, but this would be the subject for another question).
Note also that what's being said in other answers, namely something like "I'm a native speaker and the version with the clitic pronoun le sounds better to me", completely agrees to what is explained in the above cited books in reference to the case in which the presence of the clitic pronoun is (relatively) optional:
la opción del doblado es, con mucho, la preferida
and Gramática descriptiva de la lengua española adds to this statement
Véanse Silva-Corvalán 1981 para el español chileno; Bentivoglio 1978 para el Caribe y Barrenechea y Orecchia 1977 para el bonaerense.
The book Complementos argumentales del verbo: directo, indirecto, suplemento y agente by José-Álvaro Porto Dapena, gives also an example which is very similar to your sentence, in this case written without the clitic pronoun:
- Nicolás regaló una moto a su hijo
(you may also perfectly say "Nicolás le regaló una moto a su hijo").
In addition, this book provides some instances of situations that also require the presence of a clitic pronoun (this happens also in other Romance languages) without a duplication of the indirect object, namely, what are called "etic dative" ("dativo ético"), in which the presence of the clitic pronoun adds to the sentence an intensive value, expressing a greater participation of the subject in the action expressed by the verb,
- Se bebieron toda la cerveza
and "possessive dative" ("dativo posesivo"), in which the clitic pronoun adds the semantical role of possession to other noun phrase present in the sentence:
- Le llevaron el equipaje a la estación,
- Nos ocuparon los asientos.
These are examples of a complete different phenomenon because, as you can see, there is no duplication of the indirect object in the above sentences; but it is a peculiar use of dative clitic pronouns which can also give rise to wondering about the role of such pronouns.
Notice that I've not included in the above explanation what are called "left dislocation" ("dislocación a la izquierda", for instance, "A Juan le han dado un premio") and "right dislocation" ("dislocación a la derecha", for example, "No le dieron el premio, a Juan"), which are different phenomena also requiring the presence of clitic pronouns that duplicate an indirect object and that are not characteristic of Spanish language, but are also present in other Romance languages. If you need some information about them, please see the last part of this answer.