Although it may seem surprising, there is no stn named "Fukuoka stn" in "Fukuoka" where you are about to go.
"Fukuoka (prefecture)", also "Fukuoka (city)" has only "Minami-Fukuoka" and "Nishitetsu Fukuoka (Tenjin)" stns.
Minami-Fukuoka is a JR stn, Nishitetsu Fukuoka (Tenjin) is not in JR, but it is located near the JR stn.https://en.wikipedia.org/wiki/Minami-Fukuoka_Stationhttps://en.wikipedia.org/wiki/Nishitetsu_Fukuoka_(Tenjin)_Station
It is bc of this reason that you did not know the "Fukuoka" stn
in another prefecture(located in "Toyama") without knowing it due to the search at HyperDia.https://en.wikipedia.org/wiki/Fukuoka_Station
If want to go to the central stn in Fukuoka city, you had to input "HAKATA" stn.
It seems that preparation was a bit insufficient.http://www.crossroadfukuoka.jp/en/access/
Timetables of JR group will be revised around mid-March,
but if it does not change much fr the current dia(-gram),
you can be reached in about 4 hrs and full covered by Japan Rail Pass(?) like this.http://www.hyperdia.com/en/cgi/en/search.html?dep_node=TOKUSHIMA&arv_n...
There are some other methods, (except direct flight fr TKS to FUK)http://www.tokushima-airport.co.jp/en/timetables/
but transfers will also increase, and no recommend it bc it will be expenses other than Japan Rail Pass(?).
The train btw Tokushima stn and Okayama stn is not fast and there are not many till Takamatsu,
so it is one of the easy ways to take the "express bus" until "Shin Kobe stn" of Shinkansen.http://www.jr-shikoku.co.jp/bus/global/en/route/awa_ex_kobe.htmlhttp://www.hyperdia.com/en/cgi/en/search.html?dep_node=SHIN-KOBE&arv_n...
And, If you have enough time, you can cross the Tokushima port to Wakayama by Nankai ferry,http://www.nankai-ferry.co.jp/access/index.htmlhttp://www.nankai-ferry.co.jp/timetable/nobori.html
then take Nankai Railway train to KIX, finally to FUK by LCC(Peach or JetStar),https://www.kansai-airport.or.jp/en/access/trainhttp://www.fuk-ab.co.jp/english/flightSchedule/02/timetable_dom_kansai...
but you can not use Japan Rail Pass(?) for all, however, there is a possibility that it will be cheaper
than a direct flight fr TKS if you could get ticket(s) of weekday
except Fri and more special busy week GW, Obon and aroud of NewYear day.