There seem to be a lot of modern assumptions at work in your question so I'm not sure I really understand it. But I'll give it a shot.

The people who medieval Iberians called 'Franks' - that is, anyone coming from across the Pyrenees - played a very important role in both conquering and resettling the newly gained lands, the twin process we now call the Reconquista. Most of them did come from what is now France and yet calling them all French, a concept that did not really exist back then, seems to be stretching it a bit. Anyway we are talking about a lot of distinct actors in a process that spanned almost eight centuries so I would be very careful about lumping them all together.

So who exactly do you mean when you say 'the French'? The kingdom of France? Now it was indeed very eager to wage war against Albigensians in the Midi as it allowed Paris to win the South of France. As understandably, they did not want to waste resources on crusading in Spain where all the land gains would go to Castile, Leon, Aragon or Portugal anyway.

But what about other polities that existed in what is now France? Was the Carolingian Frankish kingdom 'French'? As you probably know, Charlemagne [led his armies into Spain in 778] (https://www.reddit.com/r/AskHistorians/comments/5kdnoj/how_golden_was_the_golden_age_of_islam_and_is_dr/dbouun0/) hoping to gain the Moorish strongholds on the Upper frontier in the Ebro valley and failing miserably. Or take his son, the future emperor Louis the Pious. Back when he was the Frankish king of Aquitaine Louis actually managed to conquer a couple of important cities in Spain and set up a local military administration that after the Carolingian collapse would give rise to the independent Catalan counties (here's a [comment I wrote about this] (https://www.reddit.com/r/AskHistorians/comments/5k7hs4/what_were_the_unique_responsibilities_the/) a couple of months ago). His troops were mainly Frankish but they also included a lot of Visigothic nobility, descendants of those who had fled Spain after the Islamic conquest almost a century earlier and had since settled along the French Mediterranean coast. Were these Aquitanian troops French? If they were, here you go, you have the French effectively kickstarting the Reconquista.

'The French' would also include individuals and military contingents that did not act on the authority of the king in Paris. These were very active in the Reconquest. Actually, if you believe in single important events shaping the course of a process several centuries long, it was the 'French'-led expedition against the Moorish stronghold in Barbastro in 1064 that marked an important watershed in the Reconquest. To quote an [earlier comment of mine] (https://www.reddit.com/r/AskHistorians/comments/3yencp/how_did_christians_react_to_losing_so_many/cydacgx/), the fortress was carried by an international force and the 'Franks' seem to have been responsible for the ensuing carnage. This in itself was so unusual and outrageous that the Muslim emir of Zaragoza called a jihad to recapture the town (which they did in 1065). This was the only instance of a local Muslim ruler proclaiming a jihad in the Reconquest before the Almoravids came to Spain in 1086. Notably, Charles Bishko puts the blame for turning 'the Iberian civil war of the Reconquista' into a 'Spanish crusade' squarely on the influence of the great Burgundian abbey of Cluny that emerged as the most important ecclesiastical center alongside (and in the opposition to) Rome on the European scale. So, was Cluny 'French'? If it was, you have 'the French' effectively turning the Reconquista into the religious struggle a contemporary layman thinks of when he hears the word.

Individual settlers from what is now France were instrumental in settling many towns on the frontier (with Spanish kings at times outright transplanting local French law into Spain to attract them). Individual pilgrims from (mostly) what is now France made the Camino de Santiago what it was. Teams of masons and individual sculptors and architects brought the Romanesque art style from across the Pyrenees into Spain. And so on.

P.S. To address a specific question of yours that comes across as particularly odd:

How did the naval dynamic work into this for coastal powers?

I'm definitely not an expert on the French medieval navy but in the context of the Reconquest 'French coastal powers' sounds like a joke. Most of the Reconquista did not involve a lot of naval actions anyway. But when it did, Christian Iberian rulers either hired Pisan and Genoese galleys as the Catalans did in the 12th century or relied on their own fleets later on. The Castilian naval contingent in the capture of Seville was from Galicia and the Basque provinces. And Catalans in the Crown of Aragon developed enough of a naval force to conquer the Balearic islands and basically rule the Western Mediterranean. The landings at Mallorca are supposed to have been the largest combined land-sea operation since William the Conqueror crossed the Channel in 1066. On the other hand, I'd love to be proven wrong on this but I just don't see medieval France as a seafaring power of note. Indeed, as late as the 1280s when Philippe III of France actually had the balls to attack Aragon, it was the Aragonese galleys led by Ruggero di Lauria that actually stopped the invasion, sending the entire French and Genoese fleet, such as it was, to the sea bottom off the Formigues islands. (And it was the same Aragonese squadron that had done the same twice to the entire fleet of Naples, in the Bay of Naples and a year earlier, at Malta).

Hope it helps