In a picture that they tweeted before releasing "Paris," The Chainsmokers define "Paris" as "a sentimental yearning for a reality that isn't genuine" and "an irrevocable condition for fantasy that evokes nostalgia or day dreams." The band is telling us here that "Paris" is about searching for something that isn't real and hiding from the truth of what one's life is.

We'll learn more as we study the lyrics, but as far as what they've told us, they also explained on Twitter that "Paris is a metaphor for that place u go to where everything's ok. It's subjective. It's where those who don't understand u don't exist." "Paris" sounds like a place most people would at least like to visit. It's a place one runs away to and creates a temporary, alternate reality in, and that's exactly what the song is about.
Verse 1

In the first verse of "Paris," Andrew Taggart--one of the members of The Chainsmokers--explains the basic plot of the story being told here: "We were staying in Paris / To get away from your parents." Young people often see their parents as enforcers of rules, so these two have distanced themselves from at least one person's parents in order to escape those rules, standards, or disagreements.

While the presence of Emily Warren's uncredited voice in the chorus suggests this is a romantically involved couple, nothing about the lyrics explicitly states the other person is female or a romantic interest. I'm willing to guess that this is a couple, particularly because that seems to be how The Chainsmokers write songs, but I can't definitively say.

Taggart continues singing, "And I thought, 'Wow / If I could take this in a shot right now / I don't think that we could work this out.'" This line could have two meanings: the "shot" could refer to a camera shot or to a shot of alcohol. Because of the word "take," I'm inclined to think it's the latter since we "take pictures" and don't usually say things like "take this in a shot." My theory then about these lines is that he's referring to taking the reality they've created into his body like it was a drink. But even if he did, the problems that threaten to break into their reality may still be too much for him to handle.

His female friend is "[o]ut on the terrace," and he thinks about her for a moment: "I don't know if it's fair, but I thought "How / Could I let you fall by yourself / While I'm wasted with someone else?" Essentially, he may not owe her anything, and it may not be fair to him to come help her, but despite the running from rules and the creation of unreality, they do hold onto one positive virtue, and that's loyalty to this friendship.
Chorus

Now, in the chorus of "Paris," we hear some of Warren's voice chiming in, so we know this comes from both characters' perspectives. They sing about their loyalty to each other: "If we go down, then we go down together." Perhaps they are naive and don't understand that there may be other ways to work with people, stay together, and still get what they want, but it's at least clear that they do love each other.

Taggart ponders what people will say if they "go down" (which could mean just losing good reputation or appearing to be failures in life): "They'll say you could do anything / They'll say that I was clever." They both have things going for them, and others don't want them to waste those things.

Finally, they sing, "We'll get away with everything"--an unrealistic expectation--"Let's show them we are better"--are they really better though? Through these questionable statements, the writer seems purposefully to be painting them as naive. Their desire to cling to a fake world keeps them from being able to acclimate to regular society and succeed from within the established structure.

Of course, many people have succeeded by thinking outside of the box or by stepping out of the established structure, but that the writer mentions them wanting to get away from parents suggests they are impulsive and running from something instead of being in control of where they are going.
Verse 2

In the second verse of "Paris," The Chainsmokers' narrator speaks to the female character: "You look so proud / Standing there with a frown and a cigarette / Posting pictures of yourself on the Internet." This whole song (based on the reference to parents) seems to be targeting and about millennial-aged people. This reference to posting pictures to the Internet seems to confirm it. The result is an odd depiction of a fiercely independent couple that wants to succeed and win but that is still controlled by impulses and vanity.

Taggart continues, "Out on the terrace / We breathe in the air of this small town / On our own cuttin' class for the thrill of it." This suggests that perhaps the two are in college and maybe studying in a foreign country as exchange students, which could fit easily into the "escape parents" narrative. The fact that they are "cuttin' class" further suggests their irresponsibility and naivety. Add to this the possibility the parents are paying for the girl's education, and you have an even starker picture of the fake reality they live in; if their escape is still funded by her parents, how can they really escape?

The final line of the verse is "Getting drunk on the past we were livin' in." Perhaps as they grow closer to graduation or as life continues on in general, they wish more and more to spend time in an irresponsible and impulsive past that held few problems for them.
Deeper Meaning of "Paris" by The Chainsmokers

I find it interesting that The Chainsmokers tend to ground their lessons or ideas in stories about young millennials doing crazy things. It's almost as if F. Scott Fitzgerald (The Great Gatsby) was reincarnated as a DJ duo. Fitzgerald spent a large amount of his time writing stories about the excess and emptiness of the Jazz Age in American history, and many of the empty characters were young people.

In songs like "Paris," "Closer," and "#Selfie," The Chainsmokers seem ready to point out (or at least hint) at some of the emptiness or foolishness or their own generation. This satire and self-awareness is powerful (and somewhat funny when you consider that young people running from their parents will be dancing to "Paris").

Overall, "Paris" is about a young couple that is struggling to find independence and to escape some unpleasant aspect of a reality they left behind, however temporarily. They construct a false reality and try to maintain it. Objections will try to break through, but their source of strength will be each other, and they'll maintain that relationship as they try to be something better than anyone expects they can be.