I'll try to answer your question, sorry if it doesn't satisfy you

Of course there are many ways. However, one thing that should be kept in mind is that the port cities of North Africa. especially hotbeds for corsairing activity like Algiers and Tunis are highly multilingual. Though Arabic is still the formal and widely-used language, many officials and corsairs are adept in multiple languages. Many has at least rudimentary knowledge of Spanish, French, or Italian, and most officials or high-ranking corsairs can speak multiple languages. For example, Uluc Ali can speak his native Italian, Kheireddin Barbarossa spoke Arabic, Turkish, Italian and French, and Abd al-Malik, Arab ruler of Morocco from 1576 to 1578, knew Turkish, Spanish, German, Italian, and French. Not only that, the port cities were also a very diverse place, where slaves and renegades from all corners of the world can be found. All these makes for a good environment for picking up languages.

The first and the usual way is of course to learn. English, Welsh, Scottish, Dutch, French, and many other European renegades who chose to live the "corsair dream" often has deep connections with their North African corsair counterpart. They traded with them in Mediterranean harbors, they fought in Muslim armies, joined the Barbary Corsairs in piracy and pillaging, and entered as slaves into the intimacy of Muslim life, religion, and language. Many corsairs of European origins picked up Arabic or Turkish after spending time in North Africa, the especially multilingual nature of North African port cities, with a large number of slaves and foreigners in the area is the one of the drive of this. For example Diego de Haedo reported that in Algiers Christian slaves acquired a "good knowledge of Arab and Turkish" over the course of their captivity. Humanist Bartolomaeus Georgievicz, learned Turkish, Arabic and Hebrew during his time as a slave. I think many of renowned corsairs of the Ottoman era are a good example of this, as most of them were Europeans who were enslaved before converting to Islam and picking up the language.

The reverse is also fairly common; Algerians enslaved in Spain often learned Spanish, and Thomas Phelps met an "antient Moor, who formerly had been a slave in England and spoke good English.". Because of this exchange of language, sometimes a unique situation occurs where a renegade and a North African corsair converse in a language they both learned. For example, during a raid on the coast of France, a French renegade with a convert name of Muhammad conversed with his Algerian compatriot Ali Burin in Spanish about the target of their raid. This happened because Muhammad had lived in Barcelona for some time, while Ali learned Spanish during his seven-year captivity in Mallorca and Valencia.

Another, interesting option is through a form of lingua franca. Various sources attested to the existence of a lingua franca, a kind of pidgin language used by North African corsairs to communicate with Europeans. It is known as Franco, "language of the Franks" though not necessarily meant French. It is a language with a mix of Arabic, Spanish, Turkish, Italian, and Provencal. The Sale dialect utilized Arabic, Berber, Hispano-Arabic (Morisco) and Spanish, Portuguese, French, and English. This Franco was primarily a spoken language. Its purpose was to facilitate face-to-face communication between traders, sailors, and corsairs around the Mediterranean, and we have an extensive documentation about it because not only it was widely known by intermediaries in the area, but also because it became a subject in various European plays and literature. For example, John Dryden ridiculed it in his comedy Limberham

LIMBERHAM: Now I understand him; this is almost English.

MISTRESS TRICKSY: English! away, you fop: ’tis a kind of lingua Franca, as I have heard the merchants call it; a certain compound language, made up of all tongues, that passes through the Levant.

LIMBERHAM: This lingua, what you call it, is the most rarest language! I understand it as well as if it were English; you shall see me answer him: Seignioro, stay a littlo, and consider wello, ten guinnio is monyo, a very considerablo summo

Molière’s Le bourgeois gentilhomme also has a scene where a mufti speaks Franco:

Se ti sabir, Ti respondir; Se non sabir, Tazir, tazir.

Mi star Mufti: Ti qui star ti? Non intendir: Tazir, tazir

Literature and plays aside, we have plenty of serious accounts about it. For example, the renegade Francisco Galvan relates about how his master speaks Franco. Fransisco, a domestic slave in Algiers, had taken advantage of his master's absence to go have fun with some of his fellow prisoners and get drunk. On his return, taking advantage of his drunkenness, his boss dragged him into his bed, and the husband found the couple in the act of adultery. He then seized his slave and shouted to him: "Perro sensa fida aora tomaras moro" (Faithless dog, now you will become a Muslim). Immediately improvising a conversion ceremony, he had Francisco say the profession of faith and gave him the name Ali. The next day, Fransisco, who no longer remembered the incident, did not answer when his master called him Ali, but ran up when the latter called him by his Christian first name. Taking this as proof of infidelity to the Muslim religion to which he had adhered the day before, the master threatened the latter to denounce him "presto te haré brusar" (soon, I will ensure that you are burned alive), he said to him, still in the same language.

Another example was during an inquisition trial in Ibiza on 1728 for a group of privateers who were just apprehended. Antonio Serra, a surgeon tasked for taking care of the privateers one day was approached by one of the crew. Antonio asked "Que tener Turco?" (What's wrong with you, Turk?), and the crew answered in Franco “Señor, tener calentura” (Sir, I have a fever)

To conclude, the port-cities of North Africa were a very diverse and multilingual space, which facilitated language-learning between pirates and corsairs. Those who didn't learn can still converse with their North African counterpart with a unique lingua franca known to many in the area. Still, those who didn't know either could make use of the many interpreters and those who knew the languages.

Sources/Further Reading:

Captives and Corsairs: France and Slavery in the Early Modern Mediterranean by Gillian Lee Weiss

"L'usage des langues en Méditerranée occidentale à l'époque moderne" by Natividad Planas

Pirates of Barbary: Corsairs, Conquests and Captivity in the Seventeenth-Century Mediterranean by Adrian Tiniswood

*"*Speaking in Tongues: Language and Communication in the Early Modern Mediterranean" by Eric R Dursteler

The Sultan's Renegades: Christian-European Converts to Islam and the Making of the Ottoman Elite, 1575-1610 by Tobias P. Graf

Turks, Moors, and Englishmen in the Age of Discovery by Nabil Matar