Etymology of "rapprochement" by etymonline

"bring together or into order again by urgent effort," c. 1600, from French rallier, from Old French ralier "reassemble, unite again," from re- "again" (see re-) + alier "unite" (see ally (v.)).

In Old French (and Italian), re- often appeared as ra- by confusion with the true ra- (from Latin re- + ad-), and the following consonant often was doubled; compare rabbet (a doublet of rebate), rappel (a doublet of repeal). But as ra- was not recognized in English as a prefix, words with ra- in Old French usually returned to re- in English; Rally and rabbet never were because the accent had receded. In later borrowings (rappel, rapprochement, etc.) the words tend to keep their French forms. 

Intransitive meaning "pull together hastily, recover order, revive, rouse" is from 1660s. Related: Rallied; rallying. Rallying-point "place at or about which persons come together for action" is by 1798. Rally round the flag (1862) is a line from popular American Civil War song "Battle Cry of Freedom."