ménager la chèvre et le chou

To keep two opposing sides both happy

Trying to please two people, or two opposing camps, at once without upsetting either.

Le maire essaie de ménager la chèvre et le chou dans ce débat sur le nouveau parking.

The mayor is trying to keep both sides happy in this row over the new car park.

Goes back to a riddle told since at least the 13th century, about a farmer who has to ferry a wolf, a goat and a cabbage across a river one at a time in a boat that only holds one of them alongside himself. It turns up in the Roman de la Rose. 'Ménager' here keeps its old sense of handling something carefully, as in looking after someone's feelings.