My 2 pennies about this...
1°) Normal law is a load factor control law, which means that the pilot stick or the autopilot are "asking" for a certain Nz demand, that is then computed using a number of information (like mass, CG, flaps configuration, dynamic pressure or mach number...) to give the adequate change of trajectory.
2°) Direct law is a control law that uses no information (or very little) but the gains have been set by defaut to "safe" value. It's a fixed gains mode that is adequate for a range of speeds although precision of flying is degraded and the flight domain may be restrained. Its use is related to failure modes.
3°) Normal Nz law on ground is "catastrophic" while direct law is not.
4°) The flare law is a direct law with additional damping and an additional pitch down term (increasing with time to give the pilot a "natural aircraft" behavior) that is equivalent to a direct law ajusted for low speed (no need to have it valid for 250 kt) that are activated based on RA. No RA => no flare law as such
Based on that if we loose the RA's:
1°) If landing gear is up the aircraft is entitled to think that it is not about to land and therefore there is no reason not to keep the load factor control law, whose gains do not depend on RA information.
2°) A good way to determine that landing is coming is to use landing gear information, then I do not know what the ECAM's or procedures say but the aircraft will be in direct law (or equivalent) since flare law is not available and normal law is not adequate to land.
3°) In normal mode the autopilot gains (pitch and roll) are not valid anymore (too sensitive) due to loss of RA and thus the FD information as well, which explains the loss of the APP functionality.
4°) In direct law the autopilot would still be asking for Nz while the control law is not controlling Nz anymore. Therefore it is not available either, and the "no APP mode" is sensible.
Pierre