What size forces are needed ?
what should be the German objectives in such a scenario?
can’t mines and submarines keep the RN away from the invasion force ?
You'd need at 3 to 1 odds, so you are looking at a corps at least.
And that corps is going to consist entirely of light infantry with no artillery support because Germany has zero specialized landing craft.
And more to the point, only a regiment or two are going to be landed in a single go because they can’t lift more than that.
And they are going to have to come ashore in small parties in row boats, because again, Germany doesn’t have landing craft and they aren’t going to be waltzing into Calais and using the port facilities, so they have to land across the beaches.
And no, they aren’t going to be laying mines during this landing when they are going to instead be contending with French and British mines, and their submarines were more like semi-submersible torpedo boats than the U-boats of WW2. Against the allied forces in the Channel, they’ll get wrecked.
So in the end, ”what should German objectives be in such a scenario”? Sack the officer who suggested it and don’t do it.