I could see Napoleon playing a role, if he established some sort of French presence, or at least heightened French interest, in the area.
The other ingredient would indeed have to come from some sort of Romanticism and revived interest in the Crusades, albeit, as you mention, with a decidedly Nationalist feel.
In such a timeline, it seems that the forces of Revolution had successfully co-opted the Church, using it as a way to reinforce French nationalism, rather than fight against it. Maybe in this TL, the French Church had a different head cardinal, one who successfully sensed the winds of change and led the Church on a course of reconciliation with the revolutionaries, rather than make it a monarchist (Bourbon) partisan institution.
This could mesh well with Napoleon III's ambitions, and with French anti-Semitism in the late 19th century. (Not that Palestine was mostly Jewish in those days; I'm just saying, it could fit.)
I think this idea is fantastic, if only because it draws together ideological strands that were already present, but in a totally new and unexpected way.