Some of the comments about Gare du Nord have perhaps been a little harsh; while the area is not the nicest, and the suburbs that some of the local trains serve "to be avoided", I've never felt unsafe there. I do however speak as a fluent french speaker, with no belongings (such as a camera) on display, so I appreciate that this can be different depending on your individual situation.
GNER 373, what exactly is that you're interesting in photographing? Because if it's TGVs, the grandeur of Gare de Lyon (a visit in itself!) is probably the best location. There's no barriers there (nor are there at Gare du Nord mainline platforms either, for that matter) and the clientele there are normally less intimidating.
Another one if I can suggest it is Paris St. Lazare. No TGVs to be found here, however there are two suburban lines which use the station, so you're guaranteed a train every minute or so. Plenty of loco-hauled to be found on the higher number platforms (14-19) on long-distance services to Normandy. While some of the suburbs that the local trains serve are once again in the "to be avoided" category, you should have no hassle on platform ends away from the concourse.
As for beggars coming up to people, brandishing a petition / dropping a gold ring / shouting "speak English" / making close personal contact - it's a very well known problem. I found the best way to deal with it was to avoid eye contact, and show no reaction, as if 'speak english' means nothing to you. If they persist and are really quite 'daring' and coming up to you and not getting the message, then shouting back at them in some language other than english helps - my limited (ie. 7 words in total) German did the trick when required.