The word is everywhere once you start looking to marry among French-speaking Muslims: zawaj sites, zawaj listings, "zawaj halal" groups. Its translation is nonetheless very simple, and knowing it helps you read what each of these expressions actually promises.
The translation
Zawaj (زواج) means marriage. The verb tazawwaja means to marry, zawj designates the husband and zawja the wife. When someone writes that they are "seeking zawaj", they are simply saying that they are looking to get married.
Zawaj, nikah, hlel: three words for one reality
In French-speaking usage, the three words overlap widely. Zawaj designates marriage as a state and as a project. Nikah designates more precisely the contract that founds it. Hlel is the colloquial word, derived from halal, for the religious marriage itself: we devote an article to it.
What the contract covers, on the other hand, does not vary with the vocabulary. Asked about a contract concluded without a guardian, Shaykh Abd al-Aziz Ibn Baz answers:
"Marriage brings together four people: the wali, the husband and the two witnesses. That is the legislated marriage."
Whatever word one uses, that is what one is seeking to conclude. The detail is in the conditions of marriage in Islam.
What "zawaj halal" adds
Strictly speaking, nothing: a zawaj concluded within its conditions is licit by definition. If the expression took hold online, it is by contrast. It signals a search that refuses the habits of classic dating sites: no unframed conversations, no trial relationship, a search that aims at the contract and involves it from the start.
That is the meaning we give it here: a marriage search where the guardian is present, where exchanges are framed, and where what should remain private remains private. The pages zawaj halal for a woman and zawaj halal for a man describe the process according to each person's situation.
And "zawaj sounnah"?
The expression designates the same search, with the emphasis on conformity to the Sunnah: a marriage concluded as the Prophet ﷺ taught it, adding nothing to it and taking nothing away. What that implies concretely, from the wali to the announcement, is detailed on the page marriage according to the Sunnah.
"Zawaj listings", and what a framework changes
Part of the online zawaj search happens through listings: a text describing the person, their age, their city, what they are looking for, posted in a group or on a site. There is nothing blameworthy about the format in itself, but it hands everything that follows over to private messaging, with no guardian and no outside eye.
That is precisely what Nikah replaces. The written profile plays the listing's role: religious practice, situation, project, without a photo. What follows, however, does not go private: one exchange at a time, every message read by human moderation before delivery, the sister's wali entered at sign-up and present at the mouqabalah.