No reason why we can't have both...

First, it's the 5th Hussars you will be interested in since the regiment sent two squadrons to Mexico. These were part of the 2nd
Régiment de marche along with two
Chasseurs d'Afrique squadrons. The 8th did not serve during the Mexican campaign.
The men were supposed to take the field wearing their dark blue dolmans and red trousers with fake leather booting, but the much plainer
veste (shell jacket) seems to have been a very popular garment. The pelisse was never used in Mexico, even in cold weather, so may be omitted altogether. The shako wasn't used in the field, being replaced with the kepi which was usually worn with a white cover and havelock. Both period photos and illustrations show that the sombrero was extensively worn instead of the kepi. The African army's cloth waist sash also appears to have been quite popular, and the practice of wearing it probably originated during the 5th's stint in Algeria in the late 1850's.
The pics below show a trooper in campaign dress as sketched by Benigni, a photograph of an officer circa 1863, another one of a lieutenant Teurkhauff in 1859 after his return from the Italian campaign and a scan from issue 22 of Tradition showing the Musée de l'Armée mannequin of an officer in regulation campaign dress.



Now on to the Chasseurs d'Afrique. The full dress braided jacket was never worn in the field, except by officers. The men wore their plain vestes instead, with red cavalry trousers and their distinctive
taconet, or shako, which was usually worn with a white cover and havelock in Mexico. Officers wore kepis instead, with or without a havelock.
Featured below is a very rare pic of
Chasseurs in the field during the Crimean campaign. This is how they would have looked like in Mexico, with the addition of white shako covers.

Next are period sketches of Chasseurs in Algeria in 1870 : give or take a few details, this is once again what they would have looked like on campaign in Mexico :
And finally some mannequins and a large scale figure which give a pretty good idea of the the men's equipment and accoutrements :
