Modula-2 is a much later language, from 1982, 3 years after the publication of Ada, and this is the version of Modula that has become well known. The first version of Modula has seen very little use, if any.
The first version of Modula has been conceived by Wirth while he took a sabbatical year during which he stayed at Xerox PARC. There he was impressed by the language Mesa, which already had modules.
In my opinion, Mesa was a programming language vastly better than any Modula version. Wirth however thought that Mesa was a too big language, so he attempted to design a simple language that offered some of the benefits of Mesa.
In 1976, when Wirth has designed the first (not very good) version of Modula, the DoD requirements specification process that has resulted in Ada had already passed through 3 stages: STRAWMAN (1975-04), WOODENMAN (1975-08) and TINMAN (1976-01), though the first requirements document that was close to the final language, IRONMAN, would be published only next year, in 1977. (The final DoD requirements document was STEELMAN, in 1978-06, and Ada was published one year later, in 1979-06.)
Therefore Modula had no influence on Ada.
After implementing the detailed DoD requirements (which included some influences from the language Jovial, which was used within the DoD at that time), the remainder of Ada was influenced by IBM PL/I, by Algol 68, by Pascal from Wirth, and also by Xerox Mesa, the source of inspiration for Modula. Any resemblance between Ada and Modula comes either from Pascal or from Mesa, which have been sources of inspiration for both Ada and Modula.
Xerox Mesa has been a very innovative programming language, but it is seldom mentioned today, despite being the origin of many features added to later languages, e.g. the less usual loop syntax used by Python (with ELSE; Mesa used a better keyword, FINISHED).
Unfortunately some of the best features of Mesa are not supported at all or only badly supported in most modern languages.