500 mg of elemental calcium has been show to reduce absorption of thyroxine by 20 to 25%. Evian lists the mineral content per litre as: calcium 78 mg/L, magnesium 24 mg/L, sodium 5 mg/L. So a glass of Evian is giving you 19.5 mg of calcium. Evian could reduce absorption of thyroxine by around 1%.
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Excerpt from World's Heathiest Foods...
"Due to the enormous variation in drinking water quality, it is impossible to provide any helpful nutrient profile for "water" per se. Many city tap waters will contain less than 5 milligrams of calcium per cup, less than 2 milligrams of magnesium, and only trace amounts of other minerals. As described earlier, some high-quality mineral waters will provide over 25 milligrams of magnesium per cup, over 35 milligrams of calcium, and small amounts of more than a dozen additional minerals."
I read several articles lately about Calcium interfering with levothyroxine availability. In one study calcium carbonate reduced available Levo by 20%. I think it's likely it will affect your meds, but hard to say how much.
It probably wouldn't have a huge affect, but you should drink regular water, instead of the Evian, since both calcium and magnesium affect absorption of thyroid hormones and could result in the need for higher dosages.