Finck entered the École Polytechnique in 1815, in sixth place in the ranking of students admitted that year. He graduated in 1817 and was admitted to the Artillery School, ranked third from 25 students on entry. The work of the Artillery School did not interest Finck and, in March 1818, he requested that he be allowed to enter the cavalry regiment of the Royal Guard. His request was turned down.
Finck tried again with his request in July of the same year, this time saying that if he was not allowed the move he would resign. His request was turned down and Finck resigned. However, by March 1819 Finck seems to have decided that his actions had been mistaken since he wrote asking to be readmitted to the Artillery School. This request was also turned down: Finck was clearly not very highly regarded at the Artillery School.
Returning to university, Finck entered the University of Strasbourg in 1821 studying mathematics in the Faculty of Science. He studied for his doctorate, receiving this for a dissertation Sur les mouvements de l'équateur terrestre Ⓣ in 1829.
Before completing his doctoral work, Finck began teaching mathematics at the Artillery School of Strasbourg in 1825, which does have a certain irony after his own experiences as a student at Artillery School. He was promoted to Professor of Mathematics there in 1827. He also taught at the Collège de Strasbourg from 1827, becoming a professor there in 1829.
In 1842 Finck was appointed to the chair of mathematics at the University of Strasbourg. He began to suffer from ill health in 1862 and by 1866 he was forced to take sick leave. He did not return from sick leave but retired in 1868.
Finck wrote over 20 papers and seven textbooks on mathematics. His texts include books on algebra, mechanics, geometry and analysis.
In  Finck's work on algorithms is discussed, in particular his work on analysing the Euclidean algorithm.
Article by: J J O'Connor and E F Robertson