Good luck with that. I’m assuming you mean the passé simple and the subjunctive imperfect (though the latter shows up so infrequently it’s not a worry).

I do not know of any way to specifically find such material. AFAIK only a few quirky writers or translators write in the passé composé (I have read a LOT of books and only ever seen one, though the situation might be different in, e.g. children’s lit). In any case you’ll want to focus on contemporary material.

Alternatively, you could try to sidestep the problem by avoiding the prose. You will probably never be able to escape the passé simple entirely, but if you look for bandes dessinées, of which there is a thriving market beyond the few classics that have been translated to English, you’ll find a LOT of stuff that may also have the advantage of being slightly closer to spoken French.

ETA: Now, if you aren’t looking only for fiction, I realize (as some commenters have noted) your options are a whole lot broader. Much of non-fiction is hardly ever in the passé simple (heck, history material in French is quite/most often in the present, which I’ve grown to find jarring): magazines and newspaper are full of the stuff (though you’ll find the occasional passé simple in fancy columns or editorials), and nonfiction in whatever topic you like (in my case, that’s mostly linguistics and plant science) will probably fit the bill well.

To improve your vocabulary, I warmly recommend the free anki
software. It help you review your vocabulary
daily in way that aims at optimality regarding time spent versus
number of words actually learnt, that is words that you will remember
more than a few days or weeks. Peruse the website for explanation
about its philosophy. it might seems a bit elaborated at first but it
does work (for me at least) and it is really easy to use.

Regarding press, if you do not live in France, you might be interested
in newspaper that are not to nationally centred. Check Courrier
international : it deals with
international news that are taken from foreign newspaper. As its
material is translated, it uses rather simple language but of good
quality (as opposed to some junk magazines of free newspapers such as
20 minutes).

I do not think comic books are well suited to learn a language because
they contains many partial phrases or deliberately ill constructed
ones.
Astérix is a lot of fun, especially the albums written by Goscinny
(contrariwise, avoid the very last ones like plague) but its humour
relies heavily on puns which might be difficult to grasp for a
foreigner.

Speakers at France Info (a news radio station) speak a good French
but their flow of speech might be of challenge. This remark could apply to
most radio stations.
For that matter, you might want to give RFI a try. They have a
journal en français facile (news programme in easy French).
Avoid Fun radio, Skyrock, NRJ and the like : their French is
sometimes bellow average.

Finally, as an original alternative, I would suggest interactive fictions.
They are story in which your choices affect the events. Actually they
really are text based games and were very popular a few decades ago
but still live today ; lots of games get published, some of them very
finely crafted. See here or here
for an introduction to these.
Here the text are usually simpler than in novels but the game part
makes it immersing though.
Here and there you
will find some games in French.

As others have pointed out, French fiction almost always uses the passé simple for narration. One exception is Camus’s L’Étranger (The Stranger), which is notable for its use of the passé composé. So, give that one a read, and then just take the hit read books written with the passé simple.

Le petit Nicolas doesn’t contain any passé simple. The language is at a good level for beginners, and it’s a classic of children’s fiction.

Literature is not oral speech!

Unless it is material dedicated to learning spoken French, nobody write in true spoken language.

Even in cartoon, it will be either
* Academic french, such as Tintin or Spirou
* A mix of academic for narration and spoken
* Over the top slang (e.g. le petit Nicolas)

The only true spoken french you can read is transcription of somebody speaking French.
As an example, you can watch a movie while reading only the french subtitle.

Another abundant source is transcription of french podcast.
You will find some here

Note that most of those source are formal spoken french.
Formal spoken (the way I speak to my boss) is also different from academic.

As a reminder:
* Formal academique: Cela vous convient-il?
* Formal spoken: Est-ce que cela convient?
* Informal academic: ça marche? (can also be spoken)
* Informal spoken : est-ce que ça marche?

There are all newspapers of the world of this page. you can read your favorite news from here.