CX does not have arrival lounges in either LHR or CDG.
Unless you are OW saphire, you will not have access the F gallery lounge (BA) in T5 for your MAN flight. If you are not OW saphire, you will not have access to any lounge in T5.

In CDG, you will have access to the AA lounge because you travel in C on BA. A modern and decent lounge. The CX lounge will be close early in the morning and they usually do not accept arriving pax anyway.

A very important advice is to try to make sure that you fly CX F on a 74A (77A is OK but not as good, and not currently used to LHR or CDG). AVOID the A340 as it has old F. One of the two daily CDG flight is A340 and some LHR flights have the A340s.