Having done all three and going in Summer the weather will probably be similar in terms of heat. They are all so different.
You know about the CF.
The CP from Lisbon to Porto is not really nice but has some lovely sections and some wonderful cities like Tomar and Coimbra. I have not done the variant to Fatima but will do it the next time I walk the CP. I will also do the coast and the Spiritual Variant which I didn't do when I walked the interior route. Porto is a fantastic city. It gets more crowded after Porto but nothing like the CF. My favorite town on any camino is Ponte de Lima. Lastly the warmest most friendliest and most generous people I have ever met are the people of Portugal.
The Camino from Le Puy is absolutely beautiful. More beautiful, without a doubt the the CF or CP. It is also much more difficult, especially the first couple of weeks. I am sure you will have to book in advance every day as the Gites are smaller usually but more importantly they serve dinner and often breakfast and the owners of the GItes need to know how much to prepare. If you want to just show up you will not make Gite owners happy at all!! The food in France well forget about it. It makes the food in Spain seem like you are eating at Burger King. I like the food in Spain but wowwwwww France!!!
When I walked and I doubt it has changed much, I do not think I met 5 people who spoke even passable English. Almost everyone was French with a few Germans. I walked it in 2015 and virtually everyone was a retiree walking with a small group of friends. There are no Camino Families like on the CF. It is far, far quieter. I walked in September and on most days I never saw another pilgrim except in the Gites. Most of the French people while they have credentials are walking sections of the Camino. They are nice but there is the language barrier and they tend to stick with their friends.
It is also kind of a crapshoot for when cafes and shops may be open in the villages so always have some food. I believe there were 3 days I walked the whole day with eating just an apple or banana or a candy bar as every time I got to a village the shop or cafe was closed. I speak no French at all, never really saw anyone walking around to ask so I was one hungry pilgrim at night.
Le Puy is a completely different type of Camino. Even though I spoke no French, I loved it and would do it again.
It is also the most expensive Camino of the three. But the food wow and the scenery wow wow.