It does seem obvious that Liz believes that she doesn't want to do anything that would come between Françoise and her birth mother, Thérèse. The incident last December that looked like she was trying to claim the child as her own was, to her, simply something that happened. As always, she tried to do the right thing and was misinterpreted. The problem is that Liz isn't being honest with herself and setting herself up to fail. If she'd said to herself "I can do a better job of raising Francie" and set out to live up to her belief, she'd avoid a source of future frustration. Sooner rather than later, she's going to have to stop being the Silly Sandwich Lady and become Françoise's new mother. She has to establish herself as a figure of parental authority despite her protestations otherwise. After all, she'll be the mother Thérèse cannot and perhaps will not be so she'd better arrange her thinking accordingly. Too bad Liz is a bit slow on the uptake, though. It's obvious that even though she'll be acting the part as best as she can, somebody else (April, most likely) will have to point out that Francie thinks Liz is her "real" mother.