There is no list of today of the men who died for France in Verdun. A web site in France hopes to create that list by crowdsourcing. You can help although I will suggest you do need to be fluent in French in order to contribute. Men of Memory is a virtual memorial in which users can participate through a collaborative indexing program.
The Dead for France in the First World War is a web site dedicated to indexing the French heroes of World War I and to contribute to a more precise knowledge of the conflict through its Died for France: not only the soldiers’ names, but also what losses to a unit, a type of degree, territory, a battle, a particularly deadly day. The goal is to accurately honor those killed in the Battle of Verdun.
The information already indexed is available all. A counter is shown to track the number of names indexed so far. To date, more than 435,000 records have already been indexed. If everyone contributes, all the records will be indexed and should be available by 2018.
The Mémoire de hommes et le programme d’indexation collaborative web site is available (in French) at http://goo.gl/FWLxBr. An English translation of the page made by Google may be found at https://goo.gl/f5n4By.