I have learned that in the second sentence, I can't use the present perfect as in the first one. I'd like to know the reason. Yes, she is dead. But from my point of view (my perspective), she has been to France once. Isn't that right?
My mom is still alive. She has been to France once.
My mom is dead. She went to France once.
In this sense (with respect to the specific sentence used in the question), has means the possession of something, either a quality or ownership.
It's also being used in this sentence as an auxiliary verb to been with respect to travel, and it means roughly the same thing: travel to a particular location is an experience ascribed to you (or someone).
You can't not say this about your dead mother:
✘ My mom is dead. She works at a diner.
If she's dead, she can't be working anywhere.
Nor can you say this:
✘ My mom is dead. She has a nice laugh.
If she's dead, she no longer laughs.
By the same token, you cannot say this:
✘ My mom is dead. She has been to France once.
If she's dead, she no longer has the experience of having travelled anywhere.
But both of the following are acceptable:
✔ My mom is dead. She had been to France once.
This is fine. It talks about what she experienced in the past when she was still alive to experience anything.✔ My mom is dead. Her corpse has been to France once.
While factually unusual, this is also possible. (Assuming her corpse still exists.)
This is a matter of semantics rather than syntax. There's nothing asyntactic about combining the individual words in she has been to France once. But when you add the fact that she is dead, the meaning of those exact words no longer make sense. If your mother is dead, she can no longer have anything.
