Is there a standard word or phrase in the English-speaking world to describe the angle between the fuselage and the flight path / relative wind?
It is just angle of attack.

Most anything can have an angle of attack. If you must be specific, you mention 'angle of attack of ...' Due to complexity of aerodynamics, most external elements of an airplane have their own local angle of attack. AoA sensors measure their angle of attack, and it is usually not even converted to 'wing' or 'fuselage'; it is dubbed 'indicated' or 'measured' and all limits are set with respect to that local AoA.

All these angles are usually designated as $\alpha$ (alpha), but with an appropriate index, which should always be explained in the nomenclature.

When we talk about airplane as a whole, usually the 'default' angle of attack is the one between the wind and the body frame (in the vertical plane). How body frame is defined depends on the aircraft designer, but normally X goes along the fuselage. Therefore, the angle of attack is exactly what you say: the angle between relative wind and the fuselage -- and not that of the wing (even though it is arguably more important).

Yet when we talk about aerodynamics, we may redefine the angle to mean 'angle of attack of the wing'. And even offset it to be with respect to zero lift. This is all fine as long as it's explicit. When we talk about just wing or airfoil, then the default angle of attack will be that of this object.