I do it about once a month (we've been living in Paris for a year, since DD was 4 months.)
Rule no. 1 - try to travel off peak!! Mid afternoon?
I always take the proper pushchair, rather than the light Maclaren, because then I can take the carseat, which is of course needed because Paris doesn't have lovely big black cabs. Also, I can cram more stuff under the big pushchair. Other passengers always happy to help with getting on and off, but don't expect any help from airhead staff. Some of the luggage compartments have room to lie the folded buggy down, but otherwise I just hang it by the handles from the rack in the corridor.
There are, as Prettybird says, child carriages. I have mixed feelings about them. They give DD the chance to move about, but on the other hand I find it harder to get her to settle, because there's more for her to look at.
Another top tip (not necessarily safe). If you're having trouble getting your DD to sleep, head for the space between carriages. You'll find tip-up seats opposite each other. Sit on one, put feet on the opposite one (shoes off, of course), and lie baby down with head towards your feet. It really makes the most of the train movement, and my DD normally goes off quite quickly, so I can return to our seat and lie her down there.
They're always happy to heat baby meals in the bar.
Once you're in Paris, metro is a nightmare. However buses very good. Not too hard to get onto (esp. if there are 2 of you), and every bus stop has clear maps of the different routes.
And don't forget to eat out.