The game was tied 1-1 in the eighth when the Giants used three walks to load the bases with one out and Francoeur, batting for Roger Kieschnick, sent a broken-bat liner to left field, sending home Hunter Pence.
San Francisco added to its lead later in the inning when Milwaukee third baseman Jeff Bianchi misplayed a Joaquin Arias grounder, allowing two more runs to score.
Giants starter Chad Gaudin surrendered one run on four hits over 6 1/3 innings, striking out eight.
Brewers counterpart Tyler Thornburg allowed only one unearned run on seven hits over six full innings as Milwaukee dropped the opener of a four-game series.
Notable deaths of 2014 [PHOTOS]