Out of curiosity, which of the fonts are you pairing with the German and English respectively, and of course why? For example will you be using Frutiger for German and Lexicon for English (vice versa) or a mix of both fonts for both languages?

I ask because I’m wondering whether you are looking for a gothic or traditional script style Japanese font.

Both German and English texts will be treated in the same way.
English and German texts will be only distinguished by colour - English in gray, German in black.

Some texts are describing design projects (and there are pictures on these pages) - for these texts we intend to use a sanserif typeface, whereas other texts are written rather in a narrative style - therefore we think of using a serif typeface for these texts.

I would like to have the same differentiation for these two kinds of text when choosing Japanese typefaces.

I want to avoid any connotation with Gothic scripts. The whole thing should have a contemporary feel.

When I say gothic I’m referring to what the Japanese call a sans-serif style font, i.e. Frutiger.

Try DFHS Gothic as your Frutiger equivalent…

…and DFHS Mincho for Enschedé Lexicon.

DF Kaisho is a more brush-like option that may also suit Enschedé Lexicon.

"Does anyone have any suggestions which Japanese fonts could go with these two typefaces?"

In Japan at least, when the question goes the other way around: "What Latin face goes best with Ishi Mincho or Shaken Gothic?", it is usually answered but Frutiger or Univers for their great ability to offer specific weights and widths to appear smoothly alongside the Japanese as that is used at different sizes. That's high end stuff, but the fundamental point is: if you plan on having good looking mixed scripts, choose the Kanji first, and then a Latin with the proper style set to "match" at the Kanji's different sizes. These days, with single-mastered Kanji for all sizes, I think that it goes double.

My recommends:
Frutiger/Axis
Frutiger/Shin-go

You can check some examples...

Apple uses Axis with Myliad as corporate font in Japan.
It looks very nice.
I think Axis looks good together with Humanist Sans.

Shin-go is one of the most popular sans serif typeface in Japan.
Tokyo Metro uses it with Frutiger for their new sign system.
Softbank also uses it with Frutiger

Sorry for my poor English.

I made sample.
Frutiger and Axis set togerther.

Thanks for your suggestions, guys.
This helped me a lot.