I've looked and the only thing I've found is District Council Offices - I suppose you could say District administrative centre - un chef-lieu de canton is the most important commune in the canton which is the constituency of un conseiller général/une conseillère générale. A District is a local administration in its own right with a District Council, the nearest equivalent in France is une Communauté d'Agglomération (mine is called la CAPS).
Chef-lieu de canton is a town or city that is pre-eminent, from an administrative perspective, in any given sub-division of territory. he capital of a district the next largest division, is also called a chef-lieu. While the capital of the lowest division, the municipalities is called agglomeration de chef-lieu.