As already said, Romania as a name appear on the maps at the beginning of 1860-70 decade (gradually replacing the name „Principatele Unite” - United Principalities - created by the union of Moldavia and Wallachia in 1859).
In the Napoleonic wars, Moldavia and Walachia are separate state, with large internal autonomy, but still under nominal Ottoman suzerainty. Russian influence is limiting ottoman pressure, and between 1806 and 1812 both countries were under Russian occupation. In that times their army was extremely small, more a guard for the prince, and with no real military value.
Transylvania (and other adjacent territories, now in Romania) was at that time part of Habsburg empire (Austro-Hungary date only from 1867). Some of the „grenzer” regiments were recruited in that area, but not all of them were composed of Romanians, they are also Hungarian and Székely regiments. Some of those regiments have battle honours against Napoleon (as early as Arcole if my memory is right).