2. how did climate change force the mongols south?

It became dry and the warm climatic conditions damaged the steppes and green pasture lands which made the Mongols to move towards China.

Explanation:

The tree ring data provide the necessary historic information that the Mongolian steppes were in the grip of intense drought and the mongol tribes competed for survival in those dry climatic conditions which prevailed thousand years ago. But during 1211 -25 it is observed that Mongolia had experienced an unusual rainfall  which filled the atmosphere with humidity and moisture.

This climatic conditions had made the dry steppes to fro into grasslands which fed the mongol' vital herds of  horses. It is observed that every mongol had around five horses which paved way for creation of huge cavalry force of Mongol Army. this change in climatic conditions gave rise to Genghis khan to expand his first ever huge land empire.  

the french gave their support to another tribe during he war.

pepin the short[a] (german: pippin der kurze, french: pépin le bref, c. 714 – 24 september 768) was the king of the franks from 751 until his death. he was the first of the carolingians to become king.[b][2]

the younger son of the frankish prince charles martel and his wife rotrude, pepin's upbringing was distinguished by the ecclesiastical education he had received from the monks of st. denis. succeeding his father as the mayor of the palace in 741, pepin reigned over francia jointly with his elder brother carloman. pepin ruled in neustria, burgundy, and provence, while his brother carloman established himself in austrasia, alemannia and thuringia. the brothers were active in suppressing revolts led by the bavarians, aquitanians, saxons, and the alemanni in the early years of their reign. in 743, they ended the frankish interregnum by choosing childeric iii, who was to be the last merovingian monarch, as figurehead king of the franks.