How did neo-classical elements imbue court life under Louis XIV? Refer to art, architecture, music and performance, and especially the theater of Molière.

In the following response, I'll share some thoughts on the relationship between art and absolutism, and the ways in which the absolutists made use of the arts, and to what purposes. Hopefully, this should give you some context you can then think about when trying to answer this question.
First of all, you should be aware that absolutism in the early modern era was largely about forwarding a certain image of royal authority. We see this displayed in the great palaces of the early modern era: most famously at Versailles, but one can also point towards such examples as the royal palace of Caserta (in Italy), or the royal palace in Madrid (to give only two other examples). In any of these cases, you will observe extraordinary visual opulence on a phenomenal scale, and this is all by design. These palaces are meant to invoke feelings of awe, to humble the observer with this impression of royal grandeur.
Additionally, consider that absolutist monarchies were very much performative, and to look with more detail into your example of the Bourbon court at Versailles more than verifies this. Life in Versailles was dictated by ritual, with the aristocracy of France essentially reduced to the level of sycophants, competing for the favor and attention of the King. And note, this was very much by design: the nobility represented a competing power structure which absolutist monarchs were ultimately trying to weaken and render powerless. Consider that Louis XIV rose to power in the backdrop of a civil war (the Fronde) which ultimately culminated in armed conflict between royalist forces and the arch-nobility of France. This is all very much by design.
Neo-classicism, then, represented a tool the monarchy used in order to foster an image and impression of royal power and authority. As mentioned before, we see it in the royal palaces of Europe, as well as in the artwork which fills those palaces. We can look backwards (towards the Renaissance for example), and trace this same theme across most of history, to see how art has been used as a tool by the ruling powers to assert an image of themselves conducive to their own interests: the history of patronage is practically based within this calculus. So it is with absolutist monarchs as well: absolutism draws heavily upon the use of imagery, and for a very specific effect.