Serame is a line of wines offering many varietals, including chardonnay. You can buy it at (forgive any misspelling) Le Gout du Vin in Marigot and it runs around 6-8 Euros a bottle.

Le Taitu offers this as their house wine for lunches, and Momo at Ti Bouchon keeps some on hand at times for his wines by the glass.

I find buying blindly in the grocery stores to be a frustrating experience, since there is so much bad inexpensive wine on the shelves.

And, if you are looking for better chards, I second Pony600's suggestion of Select Wine Cellar, finding Sylvain better understands our tastes in wine and can make the appropriate suggestion.

Now, you didn't hear this from me, lest the above-mentioned Sylvain permanently bar me from his shop, but try a bottle of JP Chenet to see if you like it. It runs around $5-6.