You need to clarify a few things first. Define too hot for starters. What the average Brit considers 'too hot' generally differs from what the average Floridian considers 'too hot' for beach weather. The criteria you have given re beach, shops, etc. can be matched by dozens of islands around the Mediterranean. You want to rent an 'inexpensive' house. Define inexpensive. What you think is inexpensive and what someone else things is inexpensive can be very different amounts of money.

You would do better to start with a budget number. ie.'Including travel from Paris and back (to catch our returning flight home), accommodation, food, etc. we are thinking of a budget of around $X per person for 7 nights. We would like to visit an island with good beaches but temperatures generally in the 70-80F range in mid-June. Perhaps a village a bit more off the beaten path to avoid the major hordes of tourists.'

Otherwise, your criteria allow for dozens of answers as possibilities and you might as well just Google, 'best Mediterranean Islands'. You need some more criteria to narrow down the suggestions.