The pair have been enjoying their first Cannes as a couple, and Alec provided one of the memorable moment's of this year's festival when he carried his bride-to-be up the stairs to stop her tripping over her long gown.
The 54-year-old, who has a 16-year-old daughter, Ireland, with his ex wife Kim Basinger, recently said he would love to start a family with his new love.
"Have I thought about having more kids? Oh sure, that would be great, that would be heaven, that would be fantastic," he said.
He joked: "As my friend said to me, 'When you have children, typically in a second marriage, when you're older and you get married again…
"You must always remember that you make sure the children attend a college where the commencement ceremonies are held in a facility with a wheelchair accessible ramp. "