It's no good - the thigh burn's set in and I need to take a break. We're halfway between the first and second floor of the Eiffel Tower, so I can at least pretend to be taking in the Paris skyline as I catch my breath and wait for what feels like an imminent blackout to subside.
It's our own fault. My boyfriend and I could have taken the lift, but we decided to opt the steps - the thriftiest option at five euros.
Paris might be a must-see, but the city of love doesn't come cheap.
That doesn't mean the French capital is out of bounds, though. You just have to be savvy if you don't want to be left sobbing into your baguette.
We're staying in the artistic area of Montmartre. Once home to the likes of Renoir, the area has retained its bohemian feel, with quaint cafes and cobbled streets so narrow, you can almost shake hands with the family living opposite.
It's also just a two-minute walk from white-domed Sacre-Coeur, the monumental church at the summit of Montmartre.
Climb the steps or take the funicular railway.
Either way, the views are incredible, even if you do have to jostle with the hundreds of tourists for a prime place to take your photos.
The Parisians might have a reputation for being austere but even if you're a first-time visitor, there's something comforting about the city's landscape. Perhaps it's because the iconic structures seem so familiar.
Take the Arc de Triomphe, the 19th-century monument Napoleon commissioned to celebrate his own victory - standing proud at the end of the vast Champs Elysees, and the Eiffel Tower, of course - a symbol of the city.
And you don't need to splash out to visit the famous landmarks. On the advice of some locals, we buy a book of 10 Metro tickets for just a few euros. We also walk -- a lot. Paris is laid out in wide boulevards that crisscross the Left and Right banks of the Seine.
We amble down to the famous waterway that snakes its way through the city and watch boats packed with holidaymakers drift beneath bridges, before moving on to the well-heeled 6th arrondissement (Paris is made up of 20 administrative districts) of St Germain des Pres.
Admittedly, we didn't realise how affluent the area was until my boyfriend's beer arrives, at a cost equivalent to £8. It's a one-off, we tell ourselves, and direct our attention to people watching from our street-side perch, observing the elegantly dressed waiting staff wafting around the immaculately coiffed clientele.
Thirst quenched, we make our way to the Pantheon, an impressive neoclassical dome that overlooks the city from its relatively quiet position in the Latin Quarter on the Left Bank and, behind it, find the picturesque St Etienne du Mont, where Owen Wilson waits to be taken back to the Jazz Age in Woody Allen's film Midnight In Paris.
While walking back to our flat, we come across a great little bar called Le Commerce on Rue des Martyrs in Montmartre. Bruno, the owner, couldn't have been more generous, keeping us well stocked with herby wedges, olives and cold meats, all on the house while we enjoy a frosted glass of wine that set us back around three euros each. It could have been the wine or the walking, or both, but that night, we sleep soundly.
The next day, feeling refreshed, we pick up warm baguettes and potent cheese and walk to the 17th-century Palais-Royal, for a picnic in the grounds among pink rose bushes, striking fountains and tree-lined walkways. It's also opposite the Louvre, one of the world's largest museums, which houses Leonardo da Vinci's Mona Lisa, with her all-knowing smile.
We pass the glass pyramid that dominates the courtyard at the museum's entrance and head towards the 14th-century Gothic cathedral of Notre Dame. But not without stopping off at the charming shops that sit facing the Seine along the Quai de la Megisserie.
It's here we cross the Ponts des Arts bridge where thousands of tourists used to write messages of love on padlocks and attached them to bridge, then throwing the keys into the Seine, symbolising their eternal love. The practise became so popular that in 2014, sections of the bridge had to be replaced due to the 45-tonne weight of the love locks. Authorities launched a campaign "Love Without Locks", asking couples to take selfies on the bridge instead - an even more economical option!
That evening, we journey back to Montmartre and make our way, via the steep cobbled steps and the "love wall" in Place des Abbesses (where "I love you" is daubed in an array of different languages), to the Artists' Square in Place de Tertre where the likes of Picasso used to live.
To this day, artists still set up their easels to paint tourists, but we decline the offer of an (undoubtedly unflattering) caricature in favour of light bite in a lovely old restaurant, and watch the world pass by as dusk creeps in. It's the perfect way to say au revoir to the city and return home with a few spare pennies in our pockets.
Emirates flies daily A380 services from Auckland to Paris via Dubai, with Economy Class return fares from $1,939.