Vigenere's voluminous work Traicté des chiffres (1586) is said to be like the Bible in being well-known but "generally left unread" (Mendelsohn). When browsing it in studying the historical treatment of the Vigenere cipher (Academia.edu), I found illustration of Japanese script in the addenda (not in the original edition), supplementing the illustration of various alphabets in the known world in more than 100 pages from f.287 of the original edition. (There is a title "Alphabet de la Chine, & du Giapan" on p.327 of the original edition, but the page is otherwise blank (I owe this finding to AOBANE).) The book was the first to introduce the Japanese alphabet (syllabary), if not Japanese characters, in a European book. Unfortunately, however, the information about the Japanese script is very inaccurate.
Direct communication between Japan and Europe began in the 1540s, when firearms were brought by Portuguese and Christianity was introduced by Francis Xavier (mentioned on f.CCCXXVIII v) of the Society of Jesus. In 1585, an embassy sent by daimyos arrived in Rome and was received by Pope Gregory XIII (Wikipedia). (The famous Japanese-Portuguese Dictionary was published in Nagasaki in 1603 (Wikipedia).)
Vigenere's Traicté des chiffres was the first to introduce the Japanese alphabet (syllabary) in a European book (WorldCat, citing Galland p.193). Specifically, the kana syllables according to iroha order (Wikipedia) as well as kanji characters for basic numerals are given in a table (f.CCCXXIX v to CCCXXX v). It appears these were provided by Henri de Joyeuse, comte du Bouchage (Wikipedia), mediated by a Jesuit priest Emond Auger (Wikipedia) (f.CCCXXVII).
Unfortunately, there was some mixup. As annotaed in the images, reading of the kana characters are attached to wrong columns and the values of 千 (thousand), 万 (ten thousand), and 億 (a hundred million) are incorrect.
Vigenere then presents a sample text presented "two or three years ago" to the Grand Prior of France, Charles de Valois (1573-1623) (Wikipedia), an illegitimate son of Charles IX (He was made Grand Prior of France in 1588). Vigenere acquired the copy by courtesy of "Monsieur de Roüen (Wikipedia), tres-docte & digne precepteur de ce ieune prince." The text reads
From the hand, this appears to have been written by one of the embassy who arrived in Rome in 1585 (AOBANE).
Then comes "vne copie de lettres patentes du Roy de Bongo dedans l'isle du Iappon" dated 28 August 1552 (Tenmon 21). The letter was given by Ouchi Yoshinaga. He was a brother of Otomo Sorin, the leading one of the Christian daimyos who sent the embassy to Rome in 1582. (It was Otomo Sorin who was called King of Bungo in the Jesuit records.)
This is a famous document called Daido-ji Saikyo-jo (大道寺裁許状) (Wikipedia). It grants a permission to build a church Daido-ji ("Day Dogie" in "Amangutie" (Yamaguchi) as called by Vigenere).
Vigenere was not the first to print this letter. It was first printed in 1570 in Letters of Jesuits (コインブラ版日本イエズス会書簡集). One of its later editions is available online (see p.61):
Cartas que os padres e irmãos da Companhia de Iesus escreuerão dos Reynos de Iapão & China aos da mesma Companhia da India, & Europa, desdo anno de 1549 atè o de 1580 (UC, BNP)
As it happens, Vigenere's annotation is quite inaccurate. For example, the beginning of the letter lists fiefs Zuo (周防 Suo), Nangati (長門 Nagato), Bugen (豊前 Buzen), Chicugen Caqui (筑前, 安芸 Chikuzen and Aki), Iuami (石見 Iwami), Bongo (備後 Bingo), Bichyi (備中 Bichu), but the Japanese text names only Suo. (Ouchi Yoshinaga was lord of only Suo and Nagato.) The "privileges not to be killed and not to be captured" is also not in the original. (古別府ひづる (2018)「アーネスト・サトウ著『1550年から1586年までの山口の教会の変遷』(1)」, 山口県立大学学術情報第11号 (pdf))
It appears the annotations are different from those in the Portuguese edition, but the shape of the characters of wood engraving looks similar.
There are three names in kanji.
Emond Auger is the person who mediated the acquisition of the kana syllabary (see above). Possibly, Auger was present when the embassy from Japan was received by Charles de Valois (AOBANE).
At first, I thought I found a very interesting piece of information hitherto unknown. Soon after I started searching on this material, however, it becamse clear that Vigenere's description of Japanese characters was not unknown at all.
Search for the place name "Amangutie" (Yamaguchi) returned copies of
Claude Duret, Thresor de l'histoire des langues de cest univers (Google),
which reproduces Vigenere's illustration of Japanese characters (p.913 ff.). The characters are apparently re-engraved but the errors in reading are retained.
A more relevant webpage was found when I searched for "Carolus 賀瑠" to check the reading of kanji:
デュレ『世界言語誌宝典』 (AOBANE Antiquarian Bookshop).
This page (introducing the first edition (1613) of Duret) lists further sources (which I have not seen):
新村出「世界言語志の古版本」 in 『書物礼賛』, January 1927; reprinted in 『新村出全集』第4巻, 筑摩書房 (1971, p.176) (This notes the importance of Duret's book.)
パスカル・グレオレ「いろは歌とアルファベットの邂逅」 in 小峯和明編『キリシタン文化と日欧交流』勉誠出版 (2009) (This mentions Vigenere as the oldest record of iroha syllabary extant in France.)
Fabien Simon, "Collecting Languages, Alphabets and Texts: The Circulation of 'Parts of Texts' Among Paper Cabinets of Linguistic Curiosities (Sixteenth-Seventeenth Century)" in Florence Bretelle-Establet / Stéphane Schmitt (eds.) Pieces and Parts in Scientific Texts (Springer, 2018) (Researchgate) (Judging from the abstract, what I wrote in the above may already be covered by this.)