Should we make dinner reservations in Bayeux and Paris in August?

If you're set on dining at a particular restaurant on a particular day, the answer to your question is yes.

If you don't mind being turned away and are fine with finding yourself searching for some other spot, possibly a place that microwaves its meals to bring them up to temperature, a kebab place, or the packaged salads at Monoprix, then by all means don't make a reservation.

If you will be in Bayeux on a Monday night, you will absolutely need to book ahead.

In general, in smaller touristy towns like Bayeux, it is wise to book ahead, even if just a few days before.
I do not find wandering in town while gradually getting more hungry to be a fun activity. I have made some dietary choices which mean that I cannot eat at every restaurant in France, so I am especially cautious about that and prefer to do research and give a few calls ahead.

Paris is less of an issue, unless you have a specific place in mind, tables for 2 in run-of-the-mill cafés and restaurants are usually OK. But recommended places will book up! If you want to wander without reservations, lunch is often a safer time to do so.

We were in Bayeux in mid-May, and we needed dinner reservations each night (made by our hotel Villa Lara). We watched many get turned away who did not have reservations at some of the nicer restaurants, I am sure there were some you could walk up to though. We could not get into the La Rapière restaurant all week it had been booked up for several weeks in advance. It is known as one of the better Bayeux restaurants but also very small.

Remember that many restaurants close in August and into early September. Reservations are a must; particularly at the more desirable places.