Context. The origin(s) of fast radio bursts (FRBs), mysterious radio bursts coming from extragalactic distances, remains unknown. Multiwavelength observations are arguably the only way to answer this question unambiguously. Aims. We attempt to detect hard X-ray/soft γ-ray counterparts to one of the most active FRB sources, FRB 20121102A, as well as improve our understanding of burst properties in radio through a long-term monitoring campaign using the Nançay Radio Telescope (NRT). Methods. Multiwavelength campaigns involving the International Gamma-ray Astrophysics Laboratory (INTEGRAL) satellite, the Nançay Radio Observatory, the optical telescopes at the Observatoire de Haute-Provence, as well as Arecibo were conducted between 2017 and 2019. In 2017, the telescopes were scheduled to observe simultaneously between September 24─29. We specifically used the Fast Response Enhanced CCDs for the optical observations to ensure a high time resolution. In 2019, we changed the strategy to instead conduct ToO observations on INTEGRAL and other available facilities upon positive detection triggers from the NRT. Results. In the 2017 campaign, FRB 20121102A was not in its burst active phase periodic window. We obtain a 5σ optical flux limit of 12 mJy ms using the GASP and a 3σ limit from OHP T120cm R-band image of R = 22.2 mag of any potential persistent emission not associated with radio bursts. In the 2019 campaign, we have simultaneous INTEGRAL data with at least 11 radio bursts from the NRT and Arecibo. We obtain a 5σ upper limit of 2.7 × 10−7 erg cm−2 in the 25─400 keV energy range for contemporary radio and high energy bursts, and a 5σ upper limit of 3.8 × 10−11 erg cm−2 for permanent emission in the 25─100 keV energy range. In addition, we report on the regular observations from NRT between 2016─2020, which account for 120 additional radio bursts from FRB 20121102A. We observe temporal dispersion measure (DM) variations at a level of ∆DM ∼ +2.04(4) pc cm−3/yr, in broad agreement with the literature. We also present an updated fit of the periodic active window, the emission bandwidth and the burst width distribution.