There were several possible outcomes for orphans of the rein of terror,
*surviving relatives (whether they were direct relatives who were spared persecution, or foreign relatives (not uncommon for established family's), all would have been obliged to step forward. It should also be noted the cost of raising a child was not exorbitant and would not have weighed heavily for even the petite bourgeoisie)
*Convents (many noble families had connections prior to the revolution with religious orders (financial and familial), and during their captivity and trials had access to priests and monks who could arrange guardianship after their execution in any number of French of foreign convents)
*Associates & Friends (The average noble would have toured parts of the continent through either business or pleasure and established a range of connections with their foreign peers, which would have been sustained over the years due to the art of correspondence. During the reign, many of these guardians would have been called upon to assist these enfants, and as the vast majority in foreign courts and nobles were hugely sympathetic, they would have been obliged through honour to take them in, indeed morbidly it would have been the height of fashion to have a noble orphan in London of St Petersburg...think Madonna or Jolie :S)
*Servants (guardianship was assumed by many servants, at least temporarily, as many of these people had long generational links to their respective ‘house’s’, and were fervently devoted to their masters even after they had been striped of their titles and wealth (many accounts are touching). One should also consider that the child of even a petite bourgeoisie family could have had a range of servants who were attached solely to them, including possibly a governesses, wet nurse, nursery maid, tutors and instructors, etc, and these people would have naturally felt obliged)
If all these avenues were exhausted, as noted, it is possible that the republic would have ‘taken possession’ of these orphans, and they would have been raised poorly in an orphanage or work house, although this is unlikely, as is the image of an abandoned noble child roaming provincial France in dirty and torn silk and lace.