I think the shaker is fine but I would look to maybe doing a type of wood instead of white shaker? Or would you consider a slight glaze on the white?

I think as long as you have a heavy presence of wood, you can go white cabs.. If you look at photos, the cabinets are often colored... Blue, green, yellow...I've even seen burgundy red. But wood shelves, wood work tops are key.

French country: color accents /glass doored uppers/simple stripe or check fabrics...iron hardware that makes a statement. The doorstyle could be as simple as white raised panel drawer fronts on your under counter stacks...... and do some OPEN or GLASS uppers....or shelving with interesting brackets.Depends on your budget...white painted vs oak lowers with a basic darker stain will be different price points. I'd figure out what you are willing to spend on for the cabinetry on walls [eye level] which is where details show the most. A custom hood will be pricey but can move you into your style statement in a serious way.

French Country Kitchen ideas

Here are some modern French country style kitchens.

I would consider a recessed panel cabinet door, similar to a clean-lined Shaker but with a bit more detail. Then, as others pointed out, accessorize with fabric, wall racks, shelves, and a great hood (or if the budget allows, a French range like a Lacanche or La Cornue/CornuFe).

You can see a few examples from these French sources of the Provencal style we typically think of as French country -- a slideshow:

http://www.deco.fr/photos/diaporama-10-cuisines-provencales-inspirer-d_3898/photo-p_53387

And more generically, country kitchens that tend to be less ornate:

http://www.elle.fr/Deco/Pieces/Cuisine/Des-cuisines-comme-a-la-campagne

You can see that they tend to use a lot of glazes and raised panels, but you can also see how a recessed panel and a less glazed example could be used in less Provencal influenced kitchens (in the last example). The cabinet doors with grooves are also used quite often, but that may be more detail than you might want. As you can tell in that last link, the presence of the right hardware, racks, shelves, a great stove, a great hood, and colors and fabrics.

I posted an exterior of a home in France on your other post. This pic is the kitchen in that home. I think that some open shelving, perhaps a plate rail, and even decreasing number of upper cabinets if possible will work towards your style.

My own kitchen is an older, simpler French country style with wood cabinets. My wood hood is much more simpler. I have a bit of floral fabrics and old china on the walls as well as some vintage style floral prints to add to the style. (My humble kitchen is in my "my pics" idea book.) I do love my farmhouse sink and think that can be also part of FrenchCountry style.