Recent years have seen considerable success in the generation of automatically obtained wide-coverage deep grammars for natural language processing, given reliable and large CFG-like treebanks. For research within Lexical Functional Grammar framework, these deep grammars are typically based on an extended PCFG parsing scheme from which dependencies are extracted. However, increasing success in statistical dependency parsing suggests that such deep grammar approaches to statistical parsing could be streamlined. We explore this novel approach to deep grammar parsing within the framework of LFG in this paper, for French, showing that best results (an f-score of 69.46) for the established integrated architecture may be obtained for French.