Weren't the rulers of the KOJ French? I assume there'd be some lasting French influences?
The First Crusade was largely though not entirely French nobles and their various commoner retainers--but Baldwin and presumably a substantial number of knights and commoners were Flemish. French was the dominant language and I suppose the universal one by later generations. And the native Middle Eastern people dealing with the Latins generally called them all "Franks"--"Ferengi." Italians were involved in a shipping/sea power role. Germans and English showed up in later crusades and the former established their own Crusader Order, the Teutonic Knights, but they mostly diverted later to Christianizing violently in Lithuania.
Perhaps too, English speakers might have a distorted concept of how French "Outremer" (that is, OverSeas, in French) was due to their own lords in the period having a Norman and latermore generically western French identity.
Given ongoing Rhoman power with the Latin sphere having moderately good relations--meaning the conflict might be pretty hot on some frontiers in Europe, but overall the Latin powers and Papacy are resolved to keep diplomatic channels open and some Latin states have excellent relations with the Empire (author has suggested a tendency for France in particular to play off an Eastern alliance against Germanic HRE pretensions)--as long as the KoJ remains viable on its own terms, no major dynastic civil wars or the like, no blowups with ethnic/sectarian rivalries, there will be a cultural balance between ongoing infusions of Latin contact and the importance of Eastern positive military support, which I suppose boils down to Imperial forces present to shore up the combined Latin power of the Kingdom's own urban-based knights and their supporting commoner infantry/specialists (who might be a mix of Roman Catholic, Orthodox, other Christian and perhaps peoples neither Christian nor Muslim, and conceivably loyalist Muslim and perhaps Jewish persons) plus the Roman Catholic knightly Orders (who are somewhat independent of Royal command I suppose--generally following a common policy and their envoys at the court having of course major input and guidance of Royal military and diplomatic policy--if an Order gets severely out of line that is a crisis). Waves of Crusaders coming in, particularly if the Popes coordinate with the Rhoman emperors in calling for Crusades, can be viewed as auxiliary Kingdom reinforcements, though they'd tend to be pretty unruly in lots of ways, hopefully with properly designed strategies in situations they will accept being routed in wherever their assets are most advantageous and where they will do least harm to the ongoing Kingdom institutions and diplomatic game plan. With this sort of composite force structure, the Latin high command of King and high nobles with strong ongong Western affiliations, and the Western supported Orders (with infusions of financial resources from their western chapters, some of the Orders played major roles in developing more advanced international finance and banking, plus of course I presume recruiting their Brothers mostly from Western nations) have a balance of power versus Imperial pretensions, but being dependent on the Rhoman component of force, which is allied in this model but quite independent, the Emperor if offended enough being perfectly capable of pulling them out or if the opportunity presents, turning them against the Latins to try to take over the territory directly, the Kingdom's interest is to keep relations with Constantinople very civil.
Now I have limited faith in the stability of a monarchy! The KoJ OTL seemed to be rather shrewdly arranged constitutionally, and somewhat robust against misrule, but sooner or later a dynastic succession is going to misfire with bad kings or fratricidal rivalries. The interleaved Rhoman presence may be a useful backup against this, especially if the Kingdom has an elective principle in selecting the heir (I don't recall, and generally even a kingdom with such an arrangement tends to devolve to a family succession as the elective principle gives traction to factionalists). The flip side of the Rhomans being backup to an astute consensus that a given heir or current monarch would work out badly and needs to be removed in favor of someone better suited is it gives the Rhomans leverage to manipulate dynastic crises to their advantage.
We might suppose that sooner or later, the Kingdom goes rotten and the Rhomans might then step in to incorporate it, shift the cultural balance of power toward Orthodoxy (they'd be unwise to persecute the Latins wholesale of course) and I suppose at that point the cultural and diplomatic circulation with the western sphere largely dries up, which makes the Imperial run Theme or whatever it becomes easier for the Rhomans to direct as they please, but also cuts off backup parallel support; the Empire has to shoulder the whole burden of maintaining control at its own expense entirely. Pretty much anyway, there might, depending on the circumstances, be ongoing Order support and on the inter-state diplomatic level allies in the West might still have a strong interest in helping out, maybe. It might be most astute for the Rhomans to gently intervene in Kingdom dynastic struggles and maintain the Latin nominal rule.
Meanwhile, the Empire is also a monarchy and the dynasties cannot keep rolling sixes. Sooner or later the Empire itself will go into times of trouble; hopefully for the stability of Christian dominance in Palestine this does not coincide with the Latin Kingdom also going rotten, or if Imperial takeover has already happened, the importance of keeping up the watch on the Levant leaves the region adequately strong despite serious disruption of Imperial power elsewhere.
I do think that the likely scenario is that the Muslims will be back in force at some point. For the moment the Ilkhanate is an ally but I think it is likely to be overthrown and eventually replaced with a strong resurgent Muslim order, possibly Shi'ite. Perhaps I underestimate how well the Ilkhans can Christianize their basically Persian-Mesopotamian zone--I do think Christianity will have hard sledding in Persia, but maybe if the remnant Zoroastrians can be converted and the various diverse "Nazarene" sects previously tolerated more or less united under the Khan's new brand of doctrine and organization, there might be a Christian plurality there, and possibly Mesopotamia will Christianize in larger percentages. But I also think that if this does happen, the political alliance between Constantinople and the Christianized Persian zone will deteriorate, perhaps with some domestic Persian or Kurdish or whatever dynasty that remains Christian overthrowing the Khanate, perhaps the Khans themselves assimilating over time as Normans did to England and sooner or later, under Christian or Muslim banners, the region turns back to the perennial struggle. Under either sectarian rubric, there will someday be hostile pressure from the East.
Note that if the Middle Eastern power is not Muslim, I believe the desert peoples of the Arabian zone will still remain Muslim and if both great northern rivals are Christian, might opportunistically align with one or another as the situation shifts, and perhaps act against both if they mutually weaken each other, hearkening back to the original jihad in which Arabian power overwhelmed both Rhomans and Persians back in the 7th and 8th centuries. It is not going to be easy for Christian Rhome, the Koranic ancient enemy Rum, to subdue the Arabian Red Sea coast, which currently ITTL is under Yemeni control; Muslims will tend to rally to retain Islamic control of Mecca and Medina in particular. The Arabian peninsula is liable to remain firmly Muslim even in its more agricultural zones. So if Persia-Mesopotamia, as my intuition suggests, is liable to go back to Islamic supremacy eventually, perhaps with astute tolerance of numerous non-Muslims, then they can augment their general assault on Rhome with Arabian auxiliaries who might come firmly under one Caliphate rule. And as mentioned upthread I do think that Saharan Africa will be much the same; Bedouin and Bedouin-like desert peoples will not Christianize and will be mighty hard to displace, and constantly keep pressure on the more fertile Mediterranean coast, so such outposts of Rhome as Libya and Tunis-Algeria involve ongoing draining of Imperial resources, which might be only partially covered by revenues from these lands themselves. I do agree Egypt, in the sense of the narrow Nile valley and perhaps firm holds on outposts like Siwah Oasis, might not shift back in the least and remain a firm Christian buffer between the Arabian and Saharan zones, and might manage to persist as such hived off of the Empire if it breaks up or contracts during a time of troubles as its own realm, reverting to its former role as a strong independent state echoing its status under the Ptolemies.
The Muslims however have strong interests to assert themselves to some degree in Palestine--as much as it is for Christians, it is a Holy Land to themselves as well. A very astute rule by either Latins or Rhomans might cultivate enough loyalist Muslims to defuse this pressure, permitting Muslim pilgrims to visit their own sacred sites, but that is also an obvious vulnerability, and given the OTL track record of both Rhome and the Latins I would fear the regime would draw the line (despite the OTL kingdom having had a pact with some Bedouin--after all that kingdom fell OTL!) at Muslim allegiance, persecute all Muslims sooner or later, and wall the Muslim pilgrims out. This will lend itself to a determined jihad to regain control of Palestine for Islam sooner or later, unless (as the author seems to be leaning) no stronger power than some desert nomads and trade kingdoms between the arms of the Fertile Crescent resurges. But note a Middle Eastern Ilkhanate successor, even if nominally Christian plurality ruled, might make common cause with the Arabs anyway versus Rhome; this might result, if that Persian-Mesopotamian based empire prevails in Palestine, in a multicultural Palestine as diverse as under the Ottomans, and with more Christians and possibly Jews. But also the firm rebuff of Rhoman and still less Latin power there; both Roman Catholic and Orthodox might become persona non grata there--not utterly banished or eradicated (People of the Book after all) but severely disabled and disfavored.
Such a collapse of either "Rome"s control might be the basis for Egypt hiving off as a separate Coptic-Orthodox hybrid nation. Having little traction in the Arab/other desert people regions, they might concentrate on developing ties to Ethiopia and perhaps challenging Arab power on the Red Sea, or perhaps be forced to sort of bypass by aiding Ethiopians to push control down to the African coast somewhere--that's hardly a viable major trade route though, the carriage between ports south of Somalia, if indeed these are not too Islamicized themselves to be taken or held, via Ethiopian/African Great Lakes lands to the upper navigation of the Nile is a viable major trade route only with something like railroads, I don't think suitable canal routes can be developed. So this is more a political cultural alliance than a strong economic multiplier of Egypt's basic manpower power base. Egypt might instead be able to move in on a Persian-controlled Levant.
Of course, Egypt might play these roles as a surviving exarchate of Rhoman power.
The author has mentioned a foreseen arm of Rhoman power through the Red Sea into the Indian ocean. Even with Islam itself at its weakest, this seems problematic; at best they might secure the western, African shore but Arabia will remain Muslim. Perhaps this development involves a long term detente mollifying the general Islamic resentment against "Rum" which as noted is embedded in the Koran and other foundational traditions such as the Hadith. If Rhoman authority is seen as decently respecting Islamic dignity, perhaps that opens up the Red Sea to fairly free passage of ships out of northeast Egyptian ports.
Anciently, a canal of sorts, connecting the lower Nile to the Red Sea, existed. Making a proper Mediterranean-Red Sea canal akin to Suez is not I think a reasonable thing to expect any time prior to 19th century levels of tech, but restoring and improving a riverboat suitable passage which might enable Imperial or Egyptian resources to develop a major sea trade out of a northeastern Red Sea port could be in the cards centuries before that. It would not allow for transfer of deep draft capital ships from the Med to Red seas, but it will be some time before ships of the "Age of Exploration" deep draft tall ship types, such as galleons, become mainstays of modern navies, whereas the resources to build the more typical sorts of ships such as dhows might be scarce in the northern Red Sea but could be imported up or down the Nile and over on the canal. And these smaller, lower draft large boats could perhaps transit the entire system from sea to sea.
