The way I envision the network is that the doctor was connected pre-war to the French Communist Party (already mentioned in the abortion post). Those records mysteriously burned in a completely non-suspicious fire during the chaos of the collapse. He is someone who has a good reason to be seeing a lot of different people and more importantly, to be moving in between circles include those of trusted local elites.Even if her handler (controller is something slightly different) survives and even if he confirms her cover and alibi, she's still toast from the French side. The image of her being a collaborator will be far too ingrained for any outcome other than the expected come liberation.
The question I ponder is how many other Anna Maries the doctor is running. A handler running just one would be too inefficient for words.
He is a mid-level handler with at least another layer of control above him. His method of recruiting is through his medical practice. He has feelers/observers in several villages and a trio of actively seeking information assets. Anna Marie is his prize recruit. She was mostly an observer/feeler in one of the villages but now that she is a mistress of a German officer, her penetration into the German information cycle is fairly significant.
I also agree, that if/when liberation happens and she is alive at that time, Anna Marie will be treated like shit by her neighbors until/if her actual work is revealed and vouched for. Her best bet, if she is alive, is to run like hell until she knows no one and then keep on running another fifty miles.