Authentic restaurants in Paris and Barcelona

There are way too many restaurants and tastes to give exact recommendations. I would suggest checking out:
Paris by Mouth- for authentic restaurants. They are reviewed by locals and people who are foodies. They often know the owners and chefs and know when the food is made fresh and not frozen.
For Barcelona, look at the Devour Barcelona website and check out their food blog. Their tours are great also.
Finally for Paris, check out David Lebovitz website for restaurant recommendations that fit your taste and wants.
Have fun. We were in Barcelona and Paris just two months ago.

Do you mean authentic French food in Paris and authentic Spanish food in Barcelona? Or are you looking for authentic regional restaurants in these cities? Authentic food from other parts of the world? Are you looking for traditional dishes, traditionally prepared? What does authentic even mean for you? For some people that means places with few other tourists and for others the food is the question and the number of other tourists is irrelevant.

I am interested in non-touristy French restaurants in Paris and non-touristy Spanish restaurants in Barcelona. I am a foodie :) Thanks!

Adding to what others have said, you should also look at the red Michelin and Chowhound. There are probably more tourists in these cities than locals, particularly in restaurants, so it's pretty hard to find the one diamond in the rough that no other tourists have discovered.

As a foodie I'm assuming you research food blogs before traveling. I'm not a foodie but always research them. Very helpful and informative. For Paris, David Lebovitz and Paris By Mouth are good. Can't comment on Barcelona haven't had the privilege yet.

Lastly, Conde Nast Mgazine would probably be of benefit to you. http://www.cntraveller.com/guides/europe/france/paris/where-to-eat

Bon Apetite

The word "authentic" essentially has no meaning anymore, so it's hard to know exactly what you want.

But if you want an unforgettable meal, go for the recommendations in the Michelin red guides, particularly restaurants that have reached the highly coveted star rating system (and realize that a single star rating is not the food equivalent of a one star movie, just to get a single star is a huge accomplishment for a chef). However, if your idea of "authentic" is a small mom and pop joint that hews close to a traditional recipe, a starred restaurant probably won't fit the bill. Michelin tends to reward bold innovation more than sticking to tradition. Also, with the reward of stars comes a large premium in price. The meal will be amazing, but it will hit your wallet rather hard.

But in addition to the top-of-the-class star-rated restaurants, the Michelin guides also lists recommendations (but not star ratings) for the more traditional type of restaurant I mentioned. From my experience, however, this can also serve as much of a blessing as a curse. Just like Rick Steves promoting a small, out-of-the-way gem invites a flood of Rickniks that inevitably change the character of the place, after receiving the mark of approval in the Michelin guides, a traditional-minded restaurant may find themselves overwhelmed with business from foodies that they have trouble accomodating. Particularly if it's located in or near a busy tourist area. I personally witnessed a great little restaurant in Heidelberg undergo such a transformation after it was discovered by the Michelin reviewers.

We ate twice at Cafe La Rita in Barcelona in October 2015. It was recommended to us by a young woman who worked at our hotel. We ate lunch one day and dinner another day when we were able to get a reservation. The food was fantastic - I almost would have been satisfied just by the aromas. The service was friendly and the price an excellent value. I highly recommend this restaurant and look forward to returning there.I hope you have a good time on your vacation.

I am not sure what you mean by 'authentic' but I will assume you don't want food that come from a factory, thawed, heated and put on the table for you to eat.

IMHO, you have to work hard to find bad food in France. I'm sure it can be done, but just about every place I have had a meal in France has been at least good and most very good to excellent. My worst meal in France was in Paris, where after a week of hotel breakfasts I went to a place that advertised "American Breakfast". I learned my lesson. If I want an American Breakfast I will visit some cafe or diner in the Midwest.

I like to enjoy a gourmet picnic stocked with bread, cheese and prepared foods from any of the open-air markets under the Eiffel Tower or in any of the city's parks)