This is an AWESOME idea for a thread. I have a few things to suggest for the French-speaking part of this cheese-loving country.

Geneva

Geneva has a lot to offer for free. As is true in any place, you can just walk around and explore the town. Outdoor sights include:

-the Jet d'Eau, the world's highest water fountain, which is in operation year-round whenever the weather is good. Head towards the lake and you (literally) can't miss it.
-the Botanical Gardens on Avenue de la Paix are free and open year-round during daylight hours.
-the Promenade des Bastions (near Cours des Bastions, south-west of the old town) occasionally hosts free outdoor art exhibits, and is just a nice park to walk through anyway.
-the old town (Vielle Ville) is pleasant to just walk around in.
-the city also hosts a contendor for the "World's Ugliest Cathedral Competition" in the Old Town. I'm not sure what they were thinking (or maybe the problem is that they weren't???)
-From May to October Geneve Roule rents bikes for free (which I guess, really means they just lend bikes instead of rent them.)
-If you're feeling active, you can walk along the shores of the Rhone 'til your legs give out.

Free indoor things include:

-the European Centre for Nuclear Research (CERN). The Microcosm visitors centre is free to visit (displays are in English), and if you don't mind booking three to four months in advance, three hour guided tours are available in English for free as well. Check out the website for details.
-The Maison Tavel in the Old Town is Geneva's oldest building and entrance is free.
-The Museum of Art and History (Musee d'Art et Histoire, website in French only) has free admission.

This is just a taste of what Geneva has available. Maps and tons of more info are available on the Geneva Tourism website (in English).

Lausanne

Lausanne doesn't have quite the plethora of museums, galleries and historical monuments of her bigger sister city. In Lausanne, sightseeing revolves much more around the geography, so make sure to bring your walking shoes: with a 500m elevation difference between the lake and it's northern city limit, it's a hilly city!

Free things to see/do include:

-a walk along the lakeshore in the district of Ouchy. Check out the 100-year old steamboats that are still in regular operation.
-the Lausanne Cathedral could well be one of the few Cathedrals in the world held together by duct tape. (Seriously!) The 800-odd year old building was made of stone that is dissolving faster than stonemasons can replace crumbling bricks, and duct tape is one of the measures they've resorted to for keeping pieces of it together. For an extra 2.- CHF you can climb into the belfry (232 steps), which is fun regardless, but especially worthwhile on a clear day for the views of the city, the lake and the Alps.
-the Tour de Sauvabelin at the top of town also requires a bit of stair-climbing to ascend (302 steps this time!) but it's in a nice wooded area, and again you're rewarded with views of Lausanne, Lake Geneva, the Swiss Mittelland, the Swiss Alps, the Haute-Savoie and Savoie regions of France (including Mont Blanc).

Maps and other info (and other sightseeing ideas) can be found on the Lausanne Tourism website.

The region between Lausanne and Vevey is serious wine-growing region, and there is a very nice walk through the vineyards with lots of quaint villages, stunning scenery, and ample opportunities to stop off at caves to sample the goods along the way. The best part to walk is the bit between Villette and Rivaz. For more info, contact the Lausanne tourism website.