I am assuming that you don't live in a major city in the US? If so, it wouldn't bother you, walking in the early dark evenings. Keep in mind, cities light up in the dark! It's just something to experience to feel comfortable. I think once you are in Paris and get the feel of the area, you will see people are just out enjoying their free time. I'm not sure about Xmas week, but most other times of year, people are just commuting and performing their errands. Keep in mind that other religions will be continuing on with their life or enjoying their free time as well. Later in the evening you're likely resting for the following day, anyway. Personally, I enjoy traveling in winter because there are fewer tourists crowds, and the dark evenings don't bother me solo, and the windows are pretty, etc. If you go to the theatre or symphony, etc. then just take a taxi back to your hotel if that makes you more comfortable.
I understand being fearful of the unfamiliar. Consequently, I would suggest the Rue Cler area, (which I don't usually recommend, but I stayed there on my first Paris trip in 30 years in 2000 to get my 'sea legs' back so to speak). I think you will find more Americans out and about during those hours in that area, which might make you more comfortable? Plus there are easily accessible tourist and (partially) local restaurants and food shops.
Now as far as the possibly extended strike, if you are just staying in Paris I would make that part of the excitement of the trip, as Paris will be different and the same, and not something to make me stay home. It's just part of the experience of travel and the result is sometimes fun stories.
There's no shame in being fearful of the personally unfamiliar, but just push through it, if you can. You'll feel the thrill of conquering a fear, which will make you ready for an even more adventurous trip elsewhere. IMO. Traveling solo is great fun. And the Parisian holiday decorations are lovely...slightly more elegant than other cities. Enjoy your trip!
PS, I'm mostly a vegetarian. I have no trouble eating in most countries, including France. Their produce is lovely. Their cheese is lovely. Their bread is lovely... I could go on, but won't, as I'm starting to drool. And, of course, there are so many ethnicities in Paris as well.
Also, if you can find a flight cost with which you are happy, I'd go for it. I just ran one hotel and they had plenty of openings for the week Sat. to Sat. with Xmas in-between. Have you looked at the facebook page for women over 60 traveling solo. It will give you much confidence as there you will find women traveling all over the world by themselves and loving it, along with women who want to get the nerve up to do so. I think Paris is a wonderful city in which to start your solo travels, and you can plan it this close to the event, as well with no real issues...if airfare works for you. IMO.