Without seeing responses, based on what I saw ( I went to Paris and London last November) I would go with something comfortable, low heeled or no heel, water resistant or waterproof and a bit dressy. I would stick with some type of boot for most of the daytime stuff. I really did not see many sneakers, other than leather converse, Isabel Marant and Ash look alikes.
I brought a bunch of shoes, BIG mistake, they were just dead weight. I ended up wearing a pair of SW boots I bought during day 2 of my trip for the rest of my vacation.
I could have done with the SW boots, and the pair of dressy booties I wore for the evening events I attended.
P.S. I am very happy you DS in on the mend;)