I have done a lot of walking in Paris. It used to be that the problem areas were outside the peripherique; i.e., the encircling highway.
Starting in the mid-90’s we worried a bit about traveling on the RER train between the main airport and the city center at night. It goes through one of the problem neighborhoods.
I have walked outside Gare du Nord, but mainly to make connections at Gare de L-Est. I have read reports that there was a “camp” outside Gare du Nord which should be avoided.
I have not used Saint-Lazare much. But based on its location, I would say that it should be in a quite safe neighborhood.
Paris used to be nice to walk at night along the river. I cannot say how safe it is now. They illuminate the Eiffel tower and other monuments very nicely. Last time I did a night walking tour was with my grandson about 7 years ago.
I went there a year ago. It was so crowded with tourists, you’re probably pretty safe at the main tourist areas, just keep an eye on your wallet.