It is a very low possibility POD, but...
Henri, comte de Chambord, is a bit less ossified in his prejudices and accepts the three-colored French flag when he becomes the pretender for the French throne after the abdication of Nappy III (OTL he insisted that the only flag should be the monarchist one, with the fleurs-de-lys).
So the national assembly votes a monarchist restoration in 1872 or 1873.
Henri does not have any children, and at his death in 1883 the monarchist claim for the house of Bourbon passed to Juan Carlos of Bourbon, the Carlist pretender to the Spanish throne.
If Henri is on the French throne, he might support the claim of Juan Carlos in Spain, and name him heir apparent for the French throne too.
It's all very unlikely. Just to start, I doubt there is much support in France or Spain for a dinastic union with the other. It is also almost impossible that the other European powers will accept such a union.
However, between 1883 and 1887 (when he died) Juan Carlos was the Bourbon pretender to both thrones.