If we give a look at this page on the Japan Customs site (maintained by the Ministry of Finance), we can verify the current import taxes for a wide score of products.
It is interesting to notice that the duties for WTO member Countries differs according to the wine category: if you are importing a sparkling wine you need to pay 182 yen/L, whatever the price, while with still wine the tax amount to 15% of the CIF (the value represented by the cost of the good, the insurance and the shipping fee) or 125 yen/L, whichever is the lowest (although 67 yen/L is set as a minimum).
This means that one 750 ml still wine bottle will cost an importer at most 93.75 yen of custom taxes. This amount will be the same whether you are importing a wine worth 850 yen per liter or a Domaine de la Romanée-Conti whose price tag may well be over 1 million yen.

Now, since it is very common in Japan to sell wine at a retail price three times higher than its CIF value, an importer may discount at most 93.75 yen * 3 = 281,25 yen for one bottle of still wine and 136,5 * 3 = 409,5 yen for one bottle of sparkling wine.
Although this may not seem much if you only drink stuff from 4,000 yen upward, these are pretty relevant figures when considered in the 800-2,000 yen retail price band, the most popular among casual consumers. A Gancia Prosecco for example, priced at 2,080 before taxes may go down to around 1,600-1,700 yen, which is a nice jump also from a “psychological” perspective.

However it is up to the importers to decide: on October 2019 the consumption tax for (between the others) alcoholic beverages will rise from 8 to 10%, so one strategy may be to leave the prices as they are now, reducing them at the end of the year to compensate the added cost.

According to issue number 2005 of Shuhan News (January 1st, 2019), the most important magazine for the japanese beverage industry, Suntory and Asahi are going to lower down their prices on a variety of wines: in the case of Suntory the cut will range between 20 and 140 yen, on 65 different items (starting on February 1st); for Asahi it will amount to 10 to 17% of the present retail value, on 40 different items (starting on March 1st).
Likewise the price of 70 items imported by Sapporo Breweries will be reduced between 2 and 17% from March 1st.
Other importers also planning to discount their European wines are Inaba, Mercian and Mottox  (Shuhan News 2006, January 11th 2019 issue).

“For wines above the 5,000 yen price tag there will be no change.” declared Italian wine importer Riccardo Gugole of Rotas Japan when I reached him. “Sparkling wines will be more favored, Prosecco in particular. I will lower the price of some of my wines, but I have still to decide the timing and it will not be immediate.”
“Cheapest wines on the market, those between 1.20 and 4 euros ex-cellar, will be advantaged.” confirms Federico Fanelli of Alcotrade. “They may try to eat up market shares to from Chilean wines. Furthermore in 2018 ex-cellar prices and shipment fares went up, so this EPA comes in a good moment. “

Right, Chile, the great rival. Chile has enjoyed a big success in Japan for its reasonably priced wines, which are exempted from custom taxes since 2007. Are Chilean producers worried about this new agreement?
“It is a new challenge” answered Viviana Navarrete of Leyda Wines when I interview her in September “but all challenges are good. We are really confident about the quality that we have.” And she added: “We have no fear and we are excited.”

Final words: lower priced wines will get some benefit. This may help casual consumer to approach European wines, but the effect is going to be quite limited and mitigated by the consumption tax hike in October. If you drink cheap wine you may save some bucks and I guess that some new consumer may be brought in the market.
However wine drinking in Japan will remain a pretty expensive hobby.