I am looking for information on long stays in Europe (Paris, France)
so I picked a French price for the question! Can an American take trips at
appropriate intervals from Europe to non-Shengen countries to "re-set" a tourist
visa?

I believe this question is unique on Google Answers because I don't want to
emigrate to France, I just want to visit a little bit longer.

More information: 
My boyfriend has a one year fellowship from the French Government to
work in Paris. I quit my job in late August and have enjoyed being
here, but my 89 days permitted by the Shengen agreement are nearly up
and I'm returning home to the USA. I will stay home for the holidays and then
return to France. This is where it gets complicated. I would like to
stay here (Paris) from January through August. I have found three
options. I can try to do the French long-stay visa application process in the
USA in December (and probably fail to complete in time), I can try to
find a student visa (an ideal option for me, but it appears too
expensive to take enough credit hours), or it seems possible that I
can take two trips at appropriate intervals to non-Shengen countries
to "re-set" my tourist visa. It seems from other Google Answers that
among those are two places I've always wanted to go, Iceland and the
Czech Republic. It also seems from other Google Answers that it is
important to take an airplane flight, that passport stamps aren't as
important as the little cards we fill out in flight.

Can anyone provide guidance as to how to complete the year here in
Paris? I'm specifically looking for information on whether traveling
to non-Shengan countries will suffice, but I'm open to other legal
solutions. My French friend suggested carrying around a copy of my
boyfriend's offer letter from the consulate for just the one year and talking
about *amour* if they try to kick me out... I'd like to find something
more concrete than that!

Hello  Charlie's girl
The practice of 'rebooting the visa'
 (as it is called by US expats in CR (=Czech Republic) does not require air travel.
 What decides is the entry stamp in the passport.
So as long as there is a border patrol controlling entry,
 a visit, no matter how short andno matter how you arrive,
 resulting in the stamp, will reboot your visa. 
If you decide  travel to Prague (which we heartily recommend - but
check the safety tips at)
 http://www.hedgie.org/travel/money.php
you may have to specifically ask that they stamp your passport. 
Border control is supposed to do that,
 but as American are still quite popular in CR
(House White efforts nowithstanding) many officials 'forget' to do
that, as a favor, thus allowing the visitor to stay longer than the 90
days. They will stamp your passport when you ask for it.
Enjoy, but please, do read the disclaimers and be aware that there are
no gurantees. We tested this on CR/Germany route and it worked, but
border officials are not fully dterministic system.

Hedgie

Answered my question, Thanks! I wish there could be a more "official"
answer (government website), but I guess based on the nature of this
question there will always be an element of luck to it....