The battalion to which you refer, "le 3e bataillon du marche du garde de Paris", was despatched to Spain in June 1808 and was composed of 6 companies, under the command of chef de bataillion Pierre Dariet (often given as "Daviet") du 2e bataillon du 2e régiment. They entered Spain from Bayonne on 30 June with 21 officers and 665 other ranks, with three companies from each of the two regiments. By mid-Novemebr 1808, the battalion numbered 21 officers and 555 men.
The voltiguers, under chef de bataillon Daviet, made the campaign in Portugal – attached to the état-major of the maréchal Soult for security and messenger service. In this service Daviet earned promotion to lieutenant-colonel (a rank essentially unique in the French service of the era to the garde de Paris). The other companies remained in Old Castile and Asturias under the senior captain, capitaine Davanture du 1er régiment. Strength for these in mid-February 1809 was 17 officers and 499 men. Counter-guerrilla operations and sickness left only 12 officers and 293 men fit for duty by mid-October.
The order to change from red/green habits to white ones is typically described rather vaguely as "of 1808" or "during 1808". However, we have a Spanish eyewitness at Bailén, Pedro Agustín Girón y Las Casas, el marqués de las Amarillas y el duque de Ahumada (1778-1842). He specificlly mentions the battalion of the 1er régiment in white habits trimmed red. There is no reason to think that the other two battalions sent into Spain in 1808, including the 3e bataillon du marche, would have had any different uniform.
Additionally, we have a very nice sketch from life done in 1808. Although not colored, there is no indication of shading to suggest other than a white uniform. Anyway, it is a really nice sketch.
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- Sasha
P.S. At a guess, repeat "guess"
. I would suppose that the grenadiers and two senior center companies were from the 1er régiment and that the two junior center companies and the voltiguers were from the 2e régiment.