For a general view of the Mexican Army at that time, see my recently published: "Santa Anna's Army 1821-1848" (Osprey, Elite). A good discussion of French-Mexican relations is in: Penot, Jacques, Les relations entre la France et le Mexique de 1808 et 1840 (PhD thesis, University of Paris X, 23 February 1976).
On the 27-28 November 1838 bombardment and capture of Vera Cruz by the French Navy, what Mexican sources I have seen are pretty vague. There was army and marine artillery as it was essentially a tremendous artillery duel between the castle of San Juan de Ulloa and the French fleet; also some navy sailors; some line & militia infantry. See: Miguel Lerdo de Tejeda, "Apuntes Historicos de la Heroica Ciudad de Veracruz" (Mexico, 1857).
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