The spread of influenza depends on contact among people. Contact rates are known to vary depending on the combination of age groups, which means that the age structure of a population affects the spread of influenza. We herein report how future changes in the population structure of Miyazaki Prefecture, a rural region in Japan, will affect the potential spread of influenza. We also report the results of an investigation on how future fertility changes will modify the potential spread through changes in the population structure. The basic reproduction number (R0) was used as an indicator of spread. The future population structure was projected by the cohort component method. Age-group-specific contact rates were obtained by a questionnaire survey. We found that the R0 of a new type of influenza will not change over the next 100 years if vital statistics remain constant (Scenario 0). If the total fertility rate increases by 10% or 25% from 1.7 (the level in 2011), the R0 in 2111 will be higher than that in Scenario 0. These results suggest that fertility recovery, an urgent demographic policy target in Japan, has the potential to increase the spread of influenza.