As the 89e de Ligne, it was in garrison in Valenciennes until August 1793, when the two battalions, serving in seperate divisions, took part in the invasion of Belgium and the battle of Neetwinden, and the fight at Warwick. What happens now depends on your view of history. The French Army official line is to assume the current 89e is descended from the 89e Demi-brigade de Ligne, which in its turn is descended from the 89e Demi-brigade de Bataille i.e. every 89e regiment is connected, all of which is reflected in R.E. Weaver's reply.

The actual personnel from Royal Suedois went into the 161e and 162e Demi-brigades de Bataille, so perhaps they are the true descendants. The battalion of the 161e joined the 9e Demi-brigade de Ligne in the Second Amalgame, and as such served in the Armies of Sambre-et-Meuse, Italy and the Orient; it spent most of the war in garrison in Italy until 1812, when it went to Russia, Germany and served at Waterloo. After the Restoration it became part of the Legion Departmentale of the Ain, and then the 1er Regiment de Ligne. The 162e became the 103e in 1796, and as such fought at Hohelinden and in all the campaigns of the Grande Armee, including Waterloo. It became the Legion Departmental de la Meurthe, and then the 52e Regiment de Ligne. (All of this is taken from Susane).