Crap. I thought that was 1996. After 1999, Florida State beat Virginia Tech to win the national championship.
You're correct. The Florida-FSU rematch was after the 1996 season, the same year that tOSU beat then #2 Arizona State in the Rose Bowl.
That was in the Bowl Coalition days, before the Rose Bowl joined in and it became the BCS, which started in 1998. If the BCS were in place that year, Florida State presumably would have played Arizona State in a matchup of the two unbeatens, rather than a rematch with Florida.
Here is the AP poll before the bowls were played:
<TABLE cellSpacing=0 cellPadding=0 border=0><TBODY><TR bgColor=#fafad2><TD align=right>1.
</TD><TD align=right></TD><TD align=right>1
</TD><TD></TD><TD>
Florida State (62)
</TD><TD></TD><TD align=right>11-0
</TD><TD></TD><TD align=right>1,670
</TD><TD></TD><TD>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD></TR><TR bgColor=#ffffff><TD align=right>2.
</TD><TD align=right></TD><TD align=right>2
</TD><TD></TD><TD>
Arizona State (5)
</TD><TD></TD><TD align=right>11-0
</TD><TD></TD><TD align=right>1,612
</TD><TD></TD><TD>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD></TR><TR bgColor=#fafad2><TD align=right>3.
</TD><TD align=right></TD><TD align=right>4
</TD><TD></TD><TD>
Florida
</TD><TD></TD><TD align=right>11-1
</TD><TD></TD><TD align=right>1,539
</TD><TD></TD><TD>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD></TR><TR bgColor=#ffffff><TD align=right>4.
</TD><TD align=right>
</TD><TD align=right>5
</TD><TD></TD><TD>
Ohio State
</TD><TD></TD><TD align=right>10-1
</TD><TD></TD><TD align=right>1,454
</TD><TD></TD><TD>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD><TD></TD><TD align=middle>
</TD></TR></TBODY></TABLE>