:::::Elonka, I am afraid you are effectively trying to defend your point of view with your own original research about what an alliance is or not. What is important is what scholarly sources say. If they say there was an alliance, then you have no ground to argue differently (except if this itself is referenced). In any case both views would have the right to cohexist. 
 :::::As a matter of fact, Jean Richard (among others), the leading French expert on the Mongols (in his 1996 History of the Crusades) does clearly speak about an alliance: "The Franco-Mongol alliance (...) seems to have been rich with missed opportunities" in "Histoire des Croisades", p.469, "In 1297 Ghazan resumes his projects against Egypt (...) the Franco-Mongol cooperation had thus survived, to the loss of Acre by the Franks, and to the conversion of the khan to Islam. It was to remain one of the political factors of the policy of the Crusades, until the peace treaty with the Mamluks, which was concluded in 1322 by khan Abu Said." in "Histoire des Croisades", p.468, "The sustained attacks of Baibar (...) rallied the Occidentals to this alliance, to which the Mongols also convinced the Byzantines to adhere", in "Histoire des Croisades", p.453. Both views ("an alliance", and "attempts towards an alliance") need to be handled in this article. This is the basic principle of balance and NPOV.