You are correct. It was the law school @ Columbia. He graduated from that school in 1833. After settling his grandfathers estate in 1837 he sought a commission in the Army & was posted to the
1st U.S. Dragoons, who were commanded by his uncle, Colonel
Stephen W. Kearny. Both his deceased father & grandfather were reputed to be among the wealtist men un New York, so Kearny was something of a 19th Century Patton. He could have idled his life away between the country estates and city clubs. Instead he threw himself into a military career. In 1839 he obtained orders to attend the French cavalry school at Samuar & was in combat with the Chassuers d Afrique in Algeria. Exactly how much combat is not clear. He returned to the US and the 1st Dragoons in 1840, contributed to rewriting the Army Cavalry Manual. Did some staff time with Gen Macomb & the Gen Scott. Returned to the 1st Dragoons. Resigned his commission in 1846, reapplied for a commission a few weeks later when the Mexican war started. Served in that war as a captain of Dragoons, raised and trained a troop from volunteers in Indiana, commanded Scotts bodyguard, was with the dragoons in the battle of Contreas, got his left arm shot off in the battle of Churubusco but returned to duty after recovering from the amputation.
Served with the 1st Dragoons on a frontier campaign in Oregon, then resigned his commission again in late 1851 & returned to France to rejoin the Chassuers in 1859.Evidently NY Club life did not suit him. Fought in the Italian campaign with the Chassuers & was in the battle of Soliferno. Returned to the US after two years service to France. Was recomissioned in the US Army and assigned to a brigade of infantry recently formed from volunteers & militia regiments. The regiments were of the New Jersey militia, so he may have used his NY connections to gain that & the commission.
If you made a movie of this guy who would you get to play him ? Does not matter i guess. Its to big a story to believe. Rich kid fights in three major wars for two different nations & assorted frontier campaigns on two different continents.