Logic: non-classical logics; non-normal modal logics; logical paradoxes.
Metaphysics:  meta-ontology and the methodology of ontology; theories of existence; modal metaphysics.
Epistemology: belief revision; epistemic logic; imagination and suppositional thinking; modal epistemology.
Philosophy of language: formal semantics; theories of propositional content; hyperintensional semantics.
Philosophy of computation: non-standard and parallel computation; cellular automata.

Franz works on logic, ontology, formal epistemology, the philosophy of language, the philosophy of computation. He joined the Department and the Arché Research Centre at the University of St Andrews in 2018, and he also works at the Institute for Logic, Language and Computation (ILLC), University of Amsterdam, where he has taught at the Master in Science of Logic. Before this, he was at the University of Aberdeen UK, at the Institute for Advanced Study, University of Notre Dame IN-USA, at the Sorbonne-Ecole Normale Supérieure in Paris, at the Universities of Padua, Venice and Milan-San Raffaele in Italy. His research has been funded by the British Research Council, the European Research Council, and the Leverhulme Trust. Franz is a Fellow of the Royal Society of Edinburgh and currently serves as the editor-in-chief of The Philosophical Quarterly.