English and French adapted a Latin word for torture. French uses it for working. English uses it for traveling.
That's a little simplified, but it's true. Both the French travail ("work") and English travel trace to Latin tripalium, a word related to torture. And the journey from one to the other was laborious.
Travail and travel are a classic example of "false friends" — words that look very similar but do not mean the same thing at all. You may have heard this pair called "false cognates," but they are not. Cognates are words that are related etymologically, as travail and travel are … at least historically.
Let's start with the Latin. We know from classical references that a tripalium was a device used to immobilize large, surly animals for veterinary procedures, and that it (or something of the same name) was also used to torture slaves — it may have been what they were tied to while being tortured. We can surmise that the tripalium consisted of three wooden rods: tri means "three," while palium is a derivation of palus, meaning "stake" (it also gave us impale and, through a reference to boundary stakes, beyond the pale). But we do not know what it looked like. None have survived. No one drew a picture. When the tripalium was still in use, everyone knew what it was, presumably, and once it was gone, no one wanted to memorialize it.
Except, that is, as a byword for suffering. Latin sloped into Old French in about the same way as disco sloped into house music: French even kept a sense of travail meaning "machine for restraining a large animal, such as a horse that is being shod." But in the main, the earliest uses we see in Old French of travail and its verb form, travailler — starting about a thousand years ago — use it to mean "torture" or "cause to suffer." Typically the torturer would be an abstract thing like an idea, a dream, a fascination, or an obligation, but it could also be an enemy, through war or civil oppression. And from all that, travailler also came to mean "suffer through obliged exertion": break your back or bust a gut for someone or something, figuratively speaking.
The progression took a while, but by the 1600s, notable French authors, including the great French playwrights Corneille and Molière, were using travail and travailler in pretty much all of these senses — the Dictionnaire Littré gives numerous illustrative quotes. Really, they're all one sense, aren't they? Work is suffering.
There are descendants of tripalium in several languages, each of which has made its own version: Spanish trabajo ("work"), Portuguese trabalho ("work"), Italian travaglio ("suffering, labor"), Catalan treball ("work"). It spread through the descendants of Latin, and then from French into English.
But the English version — travel — means something different, obviously. So what happened?
It's not as though English didn't have a perfectly good verb for traveling already: fare, as in seafaring and farewell, cognate with German fahren. But somehow, even in an era without airport security inspections, overpacked airplanes, and lost luggage, we decided that a French word for doing something unpleasant would be better.
Perhaps because of the effort and unpleasantness of traveling a thousand years ago, travailler had also come to mean "to travel," as in "go on a trip," in Norman French — the French spoken in Normandy, northern France. Normandy was full of people descended from Scandinavian invaders who had invaded, settled, and taken on the local language. And then they invaded England and took over there, too. It's tempting to speculate that they developed that sense specifically because when they traveled, others suffered, but there's no reason to believe that's actually how it went.
For the residents of England, Norman French became the prestige language, and eventually many of its words became part of English. English-speaking peasants raised cows, pigs, and sheep, and French-speaking lords ate bœuf (beef), porc (pork), and mouton (mutton). English-speaking peasants might have fared occasionally — they would at least have had to go to their local market towns to sell their animals — but French-speaking lords would have had the means and occasion to travel. And, over time, we kept all the luxury words. Of course we did.
We also held onto the "suffer" sense of travail: we have used travail for almost a millennium to mean "torment," "distress," "hard work," and "labor" (as in pregnancy). In fact, travel was originally spelled the same way as travail, because they were the same word. But over time, travel and travail split into two different words. (This is not the only time we've split a word into two senses and two spellings — other examples include person and parson, staunch and stanch, and to and too.)
It's not that we didn't have other luxury words we could have used instead of travel. We also took voyage and journey (from journée) from French at about the same time. But voyage originally meant a sea trip, and journée was specifically a day's travel. The earliest uses of travel/travail referred mainly to journeying outside of the country — and from England, that typically involved a journey by boat. There was no quick jaunt across a land border, as there could be from France.
And so the travails of travel became engraved in the lexicon. Over time, and as travel became a little less hazardous, we forgot the connection. Even today, it can be an ordeal … unless your work is paying for you to fly business class.