John, you are right, this would be the 75x136R 12 pdr listed by Hawkinson, because the specified case length is actually between 135 and 136 mm (5.336" = 135.53 mm). Also, the metric weight of the common shell is 5.450 Kg, which converts to 12 pounds.
Regarding the gun designation, I must point out that in French Hotchkiss literature it is indistinctly called a 75 or 76 mm L/13.5 Mountain Gun (e.g., Canon de montagne de 76 millimètres, L/13,5), so both metric caliber designations are correct in this case.
Below is a picture of the gun and a drawing of the round loaded with a common shell. The case is of the Hotchkiss separated ignition type (primerless), which means it has a vent pierced through the head that is filled with musket powder and sealed with wax. Ignition is produced by means of an external friction primer and aided by five eccentric holes surrounding the vent that lead to the propelling charge.
Note: There is a mistake in this drawing, since the groove between rim and head actually measures 0.05" (0.15+0.05+0.5+2.436+.5+1.7 = 5.336"/135.53 mm).