The French Restoration style was predominantly Neoclassic, also showing the beginnings of Romanticism in art.

Charles X Style
During his reign, the artistic style was adapted to the tastes of the new Bourgeois society. The novels of Balzac are useful to describe the comfortable apartments of the time. Charles X’s style spread from 1818 to 1834, during the Bourbon Restoration. This style could not replace completely the furnishing style from the French Empire but needs to be distinguished from the formalism of the Napoleonic era.

Image source: https://en.wikipedia.org/wiki/Charles_X#/media/File:Lefevre_-_Charles_X_(1826).jpg
Features of Charles X Style
This style was different from the formalism characteristic of the Napoleonic era, during which rigor and simplicity were fused with Greco-Roman art. Indeed, artistic fields flourished in a whole new way. In terms of furniture, this renewal was distinguished by softer lines. Even though the minimal aspect from the French Empire was still evident, forms became curvier with volutes and arabesques. Another distinction is the taste for smaller dimensions.

Image source: https://www.metmuseum.org/art/collection/search/205749
Gondola Chairs

Image source: https://en.wikipedia.org/wiki/Gondola_chair
Chair design reflected the ongoing change that wanted to make rooms more intimate and personal with conversational seating places. The predominant shape in chairs was the Gondola. The gondola design was comfortable and the smaller sizes made it easy to move. During the reign of Charles X the employment of blond woods, became popular. Dark wood marquetry with palmette motifs was used for decorative effect.
Woods

Image source: https://www.metmuseum.org/art/collection/search/206989
One of the most emblematic features of this style is the creation of “bois clairs”. At the beginning of the 19th century, dark woods were difficult to find. The furniture was adorned with precious inlays made out of dark woods used to recall foliage, to create a contrast with the veneering. Even though these decorations may look like bronze patterns from the Empire era, they were lighter and did not represent military life.
Restoration interiors
One of the best examples of Restoration-style interiors is the Charles X museum inside the Louvre, projected for the annual Salon of artists. The ceilings with compartments include paintings and rich ornamentations, featuring cornucopias, columns, and pilasters. The Restoration period saw the rise of the neo-Gothic style, which gained relevance in interior design during the 1820s. It displayed elements seen in gothic cathedrals, such as arches and rose windows that will be very popular in French salons and galleries.

Image source: https://www.metmuseum.org/art/collection/search/199071
Info sources:
https://styylish.com/restoration-furniture-style-and-design/
http://www.furniturestyles.net/european/french/restoration.html