Making my Camino Frances in July?...

Its nerve wracking, huh! Exciting, but all those unknowns give you butterflies!
The real high season is in August, when the colleges, schools and factories are closed.
Many albergues have mattresses for pilgrims who arrive when the place is full. If a place is full you can usually find a room somewhere, you'll just have to pay a little extra. You won't be alone in looking for a bed so could share with other pilgrims looking for a place to stay. If you take your cell phone you could phone ahead and book a bed in a private albergue. These are pretty much the same as any other albergue - dormitory rooms, shared ablutions etc, - but they do allow bookings in advance.
You'll be fine - just accept it all as it comes.

Keep in mind that you cannot have it all -- start late, walk all day, finish late, take lots of breaks, find a bottom bunk in the albergue you planned, stay up late, etc. Choices will have consequences. A late start means walking in the heat of the day. Walking past 3 p.m. means the beds are filling up. Arrive at a destination at 6 p.m., and even the bicyclists will be taking beds, and you may have to walk on. Health departments and fire code enforcement both reduce the number of extra beds that places can now offer after they have filled their official accommodations. There is a long-standing tradition of accommodating pilgrims, but the modern world has impacted some practices. After the first albergue fire where pilgrims cannot make it to an exit, the practice of adding mattresses to the floor will end. It is mostly a matter of "when," not "if." Tragedy seems to be just around the corner everywhere. At the moment, many places still will expand to fit the crowd, and most will allow outdoor sleeping on the available ground. Pilgrims consistently report that they always find a bed. Then the story comes along of a pilgrim who cannot find a bed for days in a row, typically in the last 100 km. Be optimistic, but also be realistic. Adjust your expectations and your actions and you will have a great time!