What modern languages to learn?

Well, German is the most important Semitic language, they say...

"what (or which?) modern foreign language...has been the most influential theologically" really depends on which theology.

For general biblical studies (this being Logos), you cannot beat German.  German also works very well for studies of Lutheran theology, and the Reformation in general.  But maybe I am biased because although English is my mother-tongue, I started studying German in primary school and continued through college.

For pastoral reasons, you may wish to study Spanish, or Chinese, modern languages with very large numbers of speakers.  (I grew up also speaking Spanish, and studied Chinese as a missionary.)

There is a lot of modern Eastern and Orthodox theology in modern Greek or Russian.  It really depends on which theology you want to study.

These days, my primary interest is Catholic theology, and I limit modern languages to English, Italian, and Latin (still used for modern liturgy and ecclesial documents; you might enjoy Traupman's "Conversational Latin for Oral Proficiency"), with a few things in Greek, Hebrew and German; I am pretty much retired from the missionary field in Asia.  Now and then I look at something in French or Spanish.

It can also be helpful to take a couple linguistics courses to look at the phenomenon of human language in general if you anticipate a long career working with multiple languages.