Recent experimental detection of noble gas (Ng) inserted fluorocarbenes, viz., FKrCF and FXeCF, which were theoretically predicted by our group earlier and very recent experimental evidences on gold-halogen analogy motivated us to explore the possibility of the existence of noble gas inserted noble metal fluorocarbene, FNgCM (Ng = Kr, Xe, and Rn; M = Cu, Ag, and Au) molecules. Ab initio quantum chemical calculations have been performed to investigate structure, stability, vibrational frequency, charge distribution and bonding analysis of FNgCM molecules by employing DFT, MP2, and CCSD(T) methods. For the purpose of comparison FNgCH molecules have also been studied. One of the important outcomes of the study is that the predicted FNgCH, FNgCCu and FNgCAg molecules are more stable in their triplet electronic states, whereas the FNgCAu molecules are found to be more stable in their singlet potential energy surface, similar to the recently observed FNgCF (Ng = Kr and Xe) molecules, although the singlet state is the lowest energy state for all the precursor carbene molecules. The gold atom behaves as a better electron donor due to the pronounced relativistic effect as compared to hydrogen, copper and silver atoms, resulting in stabilization of the singlet carbene molecule indicating halogen like chemical behavior of gold. These molecules are found to be thermodynamically stable with respect to all plausible 2-body and 3-body dissociation channels, except the one that leads to the formation of the global minimum products. However, metastable nature of the predicted molecules has been proved by studying the saddle point corresponding to the transition from the minima to the global minimum products. Sufficient barrier heights provide the kinetic stability to the predicted FNgCM molecules, which prevent them from dissociating into their respective global minimum products. All the results clearly indicate that the F-Ng bond is mostly ionic in nature with certain amount of covalent character while Ng-C bond is found to be covalent in nature. Furthermore, atoms-in-molecule (AIM), energy decomposition analysis (EDA) and charge distribution analyses suggest that the predicted FNgCM molecules essentially exist in the form of [F]δ-[NgCM]δ+. The calculated results also indicate that it may be possible to prepare and characterize the predicted molecules by suitable experimental technique(s).