non-alcoholic wine/sparkling beverages

If you go into the larger supermarkets such as Auchan, Carrefour, etc there is likely to be alongside the other wine wines and beers marked 'sans alcools', these are the non alcoholic ones. Elsewhere wine means wine with alcohol. No one is going to look askance at you drinking water or ordinary soft drinks like coke, or Orangina, and these will be on sale in all restaurants and small shops.

The Monoprix is another store with groceries - usually in the back of the store or on a separate floor level. There's also a lot of varieties of sparkling water next to the plain bottled water, and bottled sparkling water is very common to drink with meals.

French restaurants will be happy to sell you bottle water, still or "with gas". You may even be able to get tap water.

I would skip the room temperature Orangina or Coke and go with water if ice is not available when you picnic. We Americans need ice. A refillable bottle is handy for tap water from your hotel room. I drank tap water in Paris without problems.

Milk during dinner may be a problem. An American friend tried to order milk to drink with her dinner. Her waiter told her that only children drink milk with dinner.

You may even be able to get tap water.

France has had an odd-ball law since the mid-sixties that they have to give you free tap water if you ask for it. About twenty years later the law was amended to provide an exception if the intent was posted on both the exterior and interior menus. I've only noticed the exception once, so, have no idea how prevalent it is.

End of trivia report.

Try Schweppes Agrum. It's a sparkling citrus drink that is widely available in France. We love it. We also like the Lipton iced tea made with sparkling water, lemon and sugar. You can often find these things in smaller sizes (as opposed to 2 litre bottles) cold in vending machines or at places that sell sandwiches to go.

Wherever you shop you will likely be amazed at the huge variety of flavored sparkling water/drinks available. I don't drink alcohol either, so they are my main drink. BTW, I agree with RS that Badoit is the best sparking water in France.

France is one European country where not only can you easily get tap water in restaurants, for free, but you will see LOTS of French people drinking it with their meals. Just ask for "un carafe d'eau, s'il vous plais" (very roughly, "oon kaRAFF d'oh, see voo play"); if you ask just for "water" you will probably get mineral water which is not free (although I often order that as well).

In addition to the above beverage suggestions (I like Schweppes Agrum and Orangina too), there's a citron pressé, which is fresh squeezed lemon juice, sugar, and water; they are served separately and you mix to taste. This is served in cafes, not usually in restaurants.

I'll also add that, contrary to the legend that French waiters will not serve you soda with a meal, or will be rude if you try to get one, I've never had so much as a raised eyebrow when I order a Coke Zero with my lunch or dinner in a restaurant. If they don't have Coke Zero, note that a diet cola is "cola light."

Another local thing to try in cafes is a "diavolo", which is a sparkling mint-flavoured drink.

If you look behind the bar there are jugs of flavored syrups (kind of like Starbucks) that they squirt into carbonated water.

The sirops Ed mentions can also be found in most supermarkets and can be used to flavour any water you have. One thing i thought to add, yes France sells alcohol in fast food restaurants, this includes the ones in Disneyland, but it also has strict drink driving rules, I've got stopped before by the gendarmes and breathalysed, hence a lot of people do not drink alcohol during the day. You will not be alone in not drinking alcohol at any point.

During your picnic shopping, I wager you'll have lots of options and have to be careful not to buy too much. For a picnic on the Champs de Mars in front of the Eiffel Tower, the Rue Cler offers many shopping choices.

it is 'diabolo' not 'diavolo' and it can be many different flavors. When you see a bright green diabolo on a table that is mint - and is mint syrup mixed with 7 up (or what the French call lemonade) Sometimes it is done with sparkling water like perrier, but the standard mix is 'lemonade' i.e. 7 up. You can also get it in citron, and some other flavors. It is sort of my go to drink at cafes in the afternoon and I usually get lemon with the sparkling soda.

Locals usually drink tap water with meals. Even in very poncy places you will see tourists with pricey bottled water and locals with carafes of the local water. No one will bat an eye if you order it with a meal. You save quite a bit on a long trip by drinking tap water instead of bottled water. For dinner we usually get a carafe of wine and a carafe of tap water.