Gare du Nord is notorious for pickpockets and bag-snatchers, and with good reason, but so long as you don’t appear to be an easy target, you’ll be fine. Phone away, unless you absolutely have to use it, bags closed/kept close at hand, and be obviously aware of your surroundings - channel your inner meerkat. There are always so many oblivious people zombie-ing their way around GdN, and unfortunately it makes them an easy target.
I’d say Paris is broadly safe, and if you’re used to London, you’ll be grand. Years ago, I think the areas near the Eiffel Tower were somewhat gritty, I seem to remember the nearest metro station wasn’t exactly unsafe, but it wasn’t pleasant. Probably worth doing some research if you want to go there of an evening.
Service is Paris is also notorious; I’ve always found it efficient and polite, but sometimes there’s a lack of patience. If you’re going to a cafe or restaurant, particularly if it’s very busy, don’t take too long to order - ordering drinks soon after you sit will give you more time to choose your food.
The metro is a wide mix of very old and very modern lines, with accessibility to match. Line 14 is super modern, all lifts and driverless trains; others are far trickier to navigate. I believe there are metro maps which show stations with, for example, step free access from street to train. iirc, the big interchange stations, such as GdN and Chatelet-les-Halles have good accessibility, but can be crazily busy in peak hours - though it might be less so since covid.
And in Paris, as most places, even a little very basic French will earn you a lot of goodwill, particularly the niceties of please/thank you/hello/goodbye. In my experience (visiting the city and having friends there) most Parisians will speak English, but dislike the presumption. Always start with bonjour and you’ll be off to a good start.