In contrast to LFG and HPSG, there is to date no large scale Tree Adjoining Grammar (TAG) equiped with a compositional semantics. In this paper, we report on the integration of a unification-based semantics into a Feature-Based Lexicalised TAG for French consisting of around 6 000 trees. We focus on verb semantics and show how factorisation can be used to support a compact and principled encoding of the semantic information that needs to be associated with each of the verbal elementary trees. The factorisation is made possible by the use of XMG, a high-level linguistic formalism designed to specify and compile computational grammars and in particular, grammars based on non-local trees or tree descriptions.