Almost. Yes, form 2042 is your basic form - and there exists a number of additional 2042 forms for various categories of stuff that doesn't fit on the basic 4 page form. This is where to get the full array of 2042 forms:
www.impots.gouv.fr
Including the plain old vanilla 2041 NOT, which is the instructions for filing the 2042 forms. There are a variety of 2042-NOT in various languages, but these are mostly for non-residents who need to file French income taxes for whatever reason. The basic instructions only seem to be available in French. However, try dropping a pdf copy into Google Translate or a similar program and see what you get. (Haven't tried this myself. Some of the specific tax terminology may get some "odd" translations into English, but this is how we learn new specialized vocabulary.)
Actually, things tend to work the other way around. You fill out the "other" forms that you need and those are pretty good at referring you to where on the basic form (2042) you need to carry the various numbers. (Sort of how the online filing system works - so again, a good way to start to learn the French tax system.)
As a new arrival, you probably will only need the 2047 form (for foreign sourced income). So here's your link to that:
www.impots.gouv.fr
Again, try running the form and the NOT (Notice) for the form through a translation program. The instructions for the 2047 form give you some pretty specific information on how to report investment income (including bank interest) by country. The 2047 form also points out quite explicitly where to carry your various totals on the 2042 form.
Other than that, you might (at some point) have need for other forms, like the 2044 (property rental income) or 2074 (investment income, gains and losses).
Don't forget, too, that all your foreign (i.e. non-French) bank and other investment s need to be reported on forms 3916 (which go with your 2042 form). This is sort of like the FBAR requirement in the US, but you don't have to report any balance information. If you don't exactly when you opened any of your foreign s, just give it a good faith guess.
The impots.gouv.fr website has two sections - one for "International" and the other for "International (english)" which can be really useful. The stuff translated into English tends to be oriented toward non-residents filing from overseas, but there is still quite a bit of useful information there.