After leaving Place Dalida, you can continue up Rue de l'Abreuvoir until you hit La Maison Rose, and then take a left at Rue des Saules which should put you right at one of the hidden vineyards in Paris, Close Montmartre.
Almost lost in the 1930s, Clos Montmartre covers a 1,556 sqmt sloping corner of Montmartre yielding 1500 half liter bottles of red wine annually.
Here is a little history lesson for you. The hills of Montmartre were once covered with vineyards dating back to when the Romans constructed a temple dedicated to none other than the god of wine, Bacchus. During the French Revolution, everything was all destroyed, included a Benedictine abbey, but the vineyard was spared (only to be destroyed in the early 20th century to phylloxera). However, thanks to a group of dedicated local artists, Clos Montmartre was brought back to life and later saved from the urbanization of Montmartre. It was officially renewed in 1933 and is now the oldest functioning vineyard in Paris.
The wine, however, isn’t exactly your bordeaux's and rosés that often come to mind when you think of French wines, but more of a collectors items with labels designed by local artists. Each year, the bottles are auctioned off for charities during the famous five-day festival, the Fête des Vendanges. Currently funded by the Mairie de Paris, Clos Montmartre is now one of 150 vineyards in the Paris region. If you happen to be visiting during October, don’t forget to check out the dates for the festival, you won’t want to miss it!
(Pst. Since you're in the hood, make sure to check out Le Lapin Agile, a famous Montmartre Cabaret visited by the struggling artists of it’s time such as Picasso and Utrillo. It should be right behind you!)