Make the most of free first Sundays

If you get your timing right, you can visit some of the most popular museums and monuments in Paris for free, thanks to the free first Sundays programme. Among those included are tourist magnets such as the Louvre and Musee d'Orsay, as well smaller quirky spots such as the Albert-Kahn musée et jardins (a homage to gardens around the world) and the Musée de l'Assistance Publique, which celebrates the history of Paris hospitals. The free Sundays programme offers the perfect opportunity to poke your nose into some of the places you may not have considered visiting with a door tax.

• en.parisinfo.com

Parc de la Villette free open air cinema

Make the most of a summer evening in Paris and catch a free film at the open-air cinema at the Parc de la Villette. The programme runs during July and August and usually follows a particular theme. This year it's "Tous en scène'" or "Everybody on stage" and includes films such as Where the Wild Things Are, Be Kind Rewind and The Killing. It's a fantastic communal event and if you're averse to perching on the grass, you can always upgrade to a deckchair for €7.

• 19th arr, villette.com/fr

Stroll through the Jardin du Luxembourg

Photograph: Alamy

It's easy to spend an entire day wandering around this sweeping city park, which is the second largest in Paris and is the garden of the French senate. The beautifully landscaped garden, which was built in the 17th century, contains hundreds of statues, monuments and fountains – including the first model of the Statue of Liberty by Frédéric Bartholdi – which you'll stumble across as you make your way through the well kept flora. Only a short walk from many of Paris's main attractions, the park is the perfect place for any sightseer to put their feet up, read a book and enjoy a picnic.

• Rue de Médicis-Rue de Vaugirard, 6th arrondissement, senat.fr/jardin

Check out the Love Wall

Photograph: Alibi Productions/Alamy

If your stomach turns at the thought of slushy, romantic photo opportunities, then the Love Wall in Montmartre may not be for you. Still, Paris being the city of love, it's no surprise that this mural that features "I Love You" scrawled in hundreds of different languages, draws countless visitors looking for an opportunity to capture a smoochy holiday snap. The wall is the brainchild of Frederic Baron, who began collecting I love yous in 1992 before teaming up with artist and calligrapher Claire Kito who drew the mural. It's not far from the gleaming white Sacré-Coeur Basilica, an iconic Parisian attraction that can also be visited for free.

• Place des Abbesses , 18th arr, lesjetaime.com

Visit the Cathédrale Notre-Dame de Paris

View over Paris from Notre-Dame. Photograph: Sylvain Sonnet/Getty Images

One of the most popular attractions in Paris, Notre Dame cuts a dominating figure on the Île de la Cité in the middle of the Seine. The spindly gothic buttresses and magnificent stained glass windows make it as much a treat to see from the inside as out. Meanwhile, in the square and bridges around the cathedral you'll find assorted buskers, from full live bands to human statues, which always draw a crowd.

• Place Jean-Paul II, 4th arr, notredamedeparis.fr. Open daily 8am-6.45pm (7.15pm on weekends)

Explore the Père Lachaise cemetery

Woman kissing the grave of Oscar Wilde at Père Lachaise. Photograph: Peter Horree/Alamy

Behind a looming stone entrance in the 20th arrondissement lies Paris's largest cemetery, with over 100 acres of graves, tombs and memorials and 69,000 ornate (and often over-the-top) tombs of curious. It is the most visited cemetery in the world, thanks to its impressive roll call of those laid to rest here, including Georges Rodenbach, whose tomb features a bronze figure breaking out of the grave, and Oscar Wilde's, which used to be kissed by visitors with red lipstick. Jim Morrison of The Doors is also buried there; his grave is a humble stone marker that draws thousands of fans each year.

• 16 rue du Repos, 20th arr, +33 1 43 70 70 33, pere-lachaise.com. From November 6-March 15, Mon-Fri 8am-5.30pm, Sat 8.30am-5.30pm, Sun and public holidays 9am-5.30pm. From March 16-November 5 the cemetery remains open half an hour later

Admire the sculptures at Atelier Brancusi

Photograph: Marko Kudjerski/Wikimedia Commons

While a visit to the Pompidou Centre's main museum and exhibitions will cost you at least €10, the studio of Constantin Brancusi, in the same square, is free to visit. The revolutionary sculptor, who died in 1957, left his workshop and all its contents to the state and the Pompidou Centre had the studio taken apart and reconstructed in front of it in a modern pavilion. Visitors can get an impression of the space in which Brancusi worked, as well as see some of the work that helped redefine modern sculpture.

• Place Georges Pompidou, 4th arr, +33 1 44 78 12 33, centrepompidou.fr. Open daily 2pm-6pm, closed Tuesday

Walk La Promenade Plantée

Photograph: Alamy

Opened in 1993, six years before New York's similar High Line project, La Promenade Plantee is a tree-lined walkway on an old elevated railway line in east Paris. The 4.5km trail is a wonderful way to explore the city, taking you up and down staircases, across viaducts, above the streets and offering the occasional chance to wave back at the lucky Parisians whose apartments overlook it. The walkway also runs over the Viaduc des Arts, a bridge in which the arches are now occupied by galleries.

• 12th arrondissemen, promenade-plantee.org

Have a late night picnic at the Square du Vert-Galant

Photograph: Alamy

If you want to get a taste of the real Midnight in Paris, bohemian vibe, make your way down to the Square du Vert-Galant with a bottle of wine in the evening. The cosy park is situated on the western tip of the Île de la Cité and can be reached by taking the stairs down from Pont Neuf. In the summer, the park is dotted with people relaxing on the grass, enjoying the view and watching the boats sail past on either side of the island. It's not uncommon to see sparkling tea lights floating downstream with them too, adding that extra touch of Parisian magic.

• Pont Neuf, Saint-Germain-l'Auxerrois, 1st arr

Check out a fashion show at Galeries Lafayette

Photograph: Charles Platiau/Reuters

Getting a seat for Paris Fashion Week might be beyond the means of most visitors, but it's possible to get a taste of la mode every Friday afternoon at the Galeries Lafayette department store. The free shows involve professional models strutting the runway and displaying the store's fashion collection. It's still worth booking ahead to get a seat, and to confirm a show will be taking place, so contact the store in advance to get yourself a ticket.

• 40, Boulevard Haussmann, 9th arr, +33 0142 823025 or fashionshow@galerieslafayette.com, galerieslafayette.com