In June you will have no difficulty in finding hotels without booking. France is ideal for cycling given the number of cycle shops, places to eat and cheap accomodation. Bed & breakfast accomodation has grown in France of late and they are cheap and very good but there are plenty of small, family-run hotels which are really modestly priced. Organised tours are a waste of money with the choices that exist there.
I suggest Burgundy as a first tour area as it has superb scenery, good food and is reasonably compact with easy routes from Paris. Don't be timid as France was made for the bike and the French respect and admire cyclists.