Given that the monarchy was restored 20 or so years later, the royal family hardly faded into obscurity! The monarchy endured for a further 30+ years, so it could certainly be said that they took up prominent political positions. After the final overthrow of the monarchy, in 1848, there was, of course, a period during which the two competing branches of the royal family were in exile, but both are now able to be resident in France, and are hardly living in obscurity.