The actress and 127 Hours star Franco were linked in June 2013 when they were spotted visiting an art fair together in New York, and speculation soon swirled that they were preparing to walk up the aisle.
But Clarke has dismissed the rumours as ridiculous, insisting she had only met Franco on two occasions when the reports surfaced.
She tells The Observer Magazine, "I had my aunt from America calling me up and being like, 'Where's the ring?'... It's hilarious. He is, of course, beautiful. But I feel there's only a handful of women who could form an engagement after two meetings, and I'm not one of them."