have never been instructed by a conservatory trained pianist, nor attended a music school, nor analysed the origins of technical methods. can only address your question from a historical p.o.v.it seems unlikely there was a 'French' school before Chopin and his students ; the pianoforte or hammerklavier was relatively new technology and gaining popularity in Chopin's time. he was one of the first composers for the instrument (contrasted to bach, mozart, haydn who did all or much of their performing and composing on earlier keyboard instruments) who consciously addressed the technical possibilities of the instrument and the pianist. LvB was a piano teacher of course, but he believed in a doctrine of struggle ('without great struggle, there cannot be a great triumph') and making his compositions technically facile to execute was not a priority as he matured. one of Beethoven's contemporaries Friedrich Wieck was an influential teacher and promoter of the new keyboard technology, but he seems to be self taught to a large degree.what you are describing as the 'Russian school', if you went a bit deeper in its history, is probably a descendant of the teachings originated in the former Austro-Hungarian empire and its northern neighbors in the German states (Wieck's career started in Leipzig). there is a legion of pianists from the twentieth century onward whose 'school' goes back to Liszt's students, and Liszt himself studied with LvB's disciple Czerny, as you probably know. as far as post-Revolution Soviet piano methods, two of their influential teachers are the father and son of Heinrich and Stanislav Neuhaus. Hungary to this day still considers itself to have its own school of pianism.getting back to your comparison of the Russian and French schools, at one time von Bulow (himself a student of Wieck) compared Saint Saens to Liszt, and believed the former to be superior technically and as an improvisor at the piano. Saint Saens had learned the instrument by the age of three from a great aunt. Debussy learned piano from one of Chopin's students. [Cortot, an influential teacher in the 20th century, studied in Paris under one of Chopin's pupils]. there is yet a third school of pianism (if we consider the Russians closely related to the German/Hungarian sources), Italian. the pianoforte itself was developed in Florence, in part due to the patronage of the de'Medicis. Clementi was considered the technical equal of Mozart and Beethoven, and someone who is better versed in piano pedagogy might be able to explain what some of the distinctions between Italian methods and those from further north.
Topic: French vs. Russian vs Other school of technique 