The following is a list of the playable factions in the European Campaigns of LME 4.2. I decided to post it because I couldn't find this information anywhere, and it may be useful to someone.
1792 European Campaign
Duchy of Mecklenburg-Schwerin
Commonwealth of Poland
Electorate of Saxony
Kingdom of Sicily
Portuguese Empire
Republic of Venice
Denmark-Norway
Electorate of Bavaria
Papal States
Kingdom of Sardinia
Landgraviate of Hesse-Kassel
Kingdom of Sweden
Duchy of Milan
Seven United Netherlands (Dutch Republic)
Republic of the Swiss (Swiss Confederacy)
French Republic
Habsburg monarchy (Austrian Empire)
United Kingdom
Kingdom of Prussia
Russian Empire
Ottoman Empire
Kingdom of Spain
1796 European Campaign
Duchy of Mecklenburg-Schwerin
Electorate of Saxony
Kingdom of Sicily
Kingdom of Sardinia
Republic of Venice
Electorate of Bavaria
Denmark-Norway
Portuguese Empire
Helvetic Republic
Landgraviate of Hesse-Kassel
Duchy of Milan
Electorate of Württemberg
Papal States
Batavian Republic
Kingdom of Sweden
Duchy of Oldenburg
French Republic
Habsburg monarchy (Austrian Empire)
United Kingdom
Kingdom of Prussia
Russian Empire
Ottoman Empire
Kingdom of Spain
1805 European Campaign
Duchy of Mecklenburg-Schwerin
Landgraviate of Hesse-Kassel
Kingdom of Sicily
Swiss Confederacy
Electorate of Saxony
Electorate of Bavaria
Denmark-Norway
Portuguese Empire
Papal States
Kingdom of Sardinia
Kingdom of Sweden
Kingdom of Italy
Batavian Republic
Electorate of Württemberg
Duchy of Oldenburg
French Empire
Austrian Empire
United Kingdom
Kingdom of Prussia
Russian Empire
Ottoman Empire
Kingdom of Spain
1807 European Campaign
Kingdom of Sweden
Duchy of Warsaw
Kingdom of Saxony
Duchy of Mecklenburg-Schwerin
Kingdom of Sicily
Portuguese Empire
Denmark-Norway
Kingdom of Bavaria
Kingdom of Westphalia
Kingdom of Sardinia
Grand Duchy of Hesse
Papal States
Kingdom of Württemberg
Duchy of Oldenburg
Kingdom of Naples
Kingdom of Italy
French Empire
Kingdom of Holland
Swiss Confederacy
Austrian Empire
United Kingdom
Kingdom of Prussia
Russian Empire
Ottoman Empire
Kingdom of Spain
1812 European Campaign
Duchy of Mecklenburg-Schwerin
Grand Duchy of Hesse
Portuguese Empire
Kingdom of Sardinia
Kingdom of Sicily
Duchy of Warszaw
Kingdom of Westphalia
Kingdom of Bavaria
Swiss Confederacy
Kingdom of Naples
Kingdom of Holland
Kingdom of Italy
Kingdom of Saxony
Kingdom of Württemberg
Denmark-Norway
Kingdom of Sweden
French Empire
Austrian Empire
United Kingdom
Kingdom of Prussia
Russian Empire
Ottoman Empire
Kingdom of Spain
1813 European Campaign
Duchy of Mecklenburg-Schwerin
Kingdom of Belgium
Duchy of Warsaw
Kingdom of Westphalia
Kingdom of Naples
Denmark-Norway
Portuguese Empire
Kingdom of Bavaria
Kingdom of Saxony
Kingdom of Sicily
Grand Duchy of Hesse
Kingdom of Sardinia
Kingdom of Sweden
Kingdom of Holland
Kingdom of Italy
Kingdom of Württemberg
Swiss Confederacy
French Empire
Austrian Empire
United Kingdom
Kingdom of Prussia
Russian Empire
Ottoman Empire
Kingdom of Spain
1815 European Campaign
Kingdom of Naples
Kingdom of Sicily
Kingdom of Bavaria
Norway
Grand Duchy of Hesse
Kingdom of Saxony
Kingdom of Hanover
Kingdom of Poland
Kingdom of Belgium
Kingdom of Sardinia
Denmark-Norway
Principality of Serbia
Kingdom of the Netherlands
Courland
Hellenic State
Kingdom of Sweden
Kingdom of Württemberg
Kingdom of France
Portuguese Empire
French Empire
Austrian Empire
United Kingdom
Kingdom of Prussia
Russian Empire
Ottoman Empire
Kingdom of Spain