We used ¹H nuclear magnetic resonance (NMR) to study the phase transitions and molecular dynamics in a characteristic ferroelectric liquid crystal with a carbon number n = 7, S-2-methylbutyl 4-n-heptyloxybiphenyl-4'-carboxylate (C7). The results were compared with those of our recent work on S-2-methylbutyl 4-n-octanoyloxybiphenyl-4'-carboxylate (C8), with a carbon number n = 8. While the recrystallization and isotropic phase transitions exhibited a first-order nature in the 1H NMR spin-lattice and spin-spin relaxation measurements, a second-order nature was shown at the Sm-A - Sm-C^* liquid crystalline phase transition. A soft-mode anomaly arising from the tilt angle amplitude fluctuation of the director, of which only a hint had been noticed in the C8 system, was manifested in the C7 system at this transition.