I travel alone a lot, I'm 63.
I've stayed twice in Paris in an apartment , each time for two weeks.
No problems at all, and always felt safe.
I did get the flu the first time and was housebound, alone, and quite sick for 3 days; but I had managed to get in plenty groceries, and always travel with a full medicine kit, so I was alright.
Now that apartments need registration codes to be fully legal rentals , I'd be a bit more cautious renting one.
How about staying in a small hotel for one week, then trying a different hotel and area for the second week?
Or an apart/hotel is a very good idea.
As for being a woman alone in Paris, I felt safe always; and walked, and took the Metro and buses everywhere.
I too have high school French; but any Smartphone will help you with translating.
I actually took a weeks French classes in Paris the first time I was there, and really enjoyed it!
You can kind of pretend you live there.
You will just love it, and feel very brave after your trip; then you can do it all again another time!