I think any standard introductory physics textbook will cover both topics.
Of course, if you really want to know what vectors are, you will have to look in differential geometry where they are defined rigorously through the transformation properties of their components. It is there that you realize vectors are really just rank 1 contra variant tensors. For that, I recommend: https://www.amazon.com/dp/0486640396/?tag=pfamazon01-20&tag=pfamazon01-20
Good thing you are French too, because this book is written in English.
One key point of friction is that it is a measured quantity and there are two variants static and kinetic friction (aka dynamic friction) with static being the higher value as a reluctance of something to slide is higher than when it is sliding.
The normal force is used because frictional force is related to the mass of the object, the acceleration of gravity and the frictional coefficient so the normal force vector provides the magnitude of the force and the projection of it on the inclined plane provides the actual frictional force for the problem.