In this paper, a 2x2 single-mode coupler based on indium fluoride optical fibers from Le Verre Fluore (Bruz, France) is designed and characterized in the mid-infrared wavelength range. Coupled mode theory and finite element method are employed for its design. The 2x2 optical fiber coupler is fabricated via fused biconical tapering technique, employing a Vytran (R) GPX-2400 glass processing system. The primary constraint associated with the limited temperature range for processing indium fluoride optical fibers has been successfully addressed. Two identical fluoroindate (InF3) step-index optical fibers having a core diameter d(co) = 7.5 mu m, cladding diameter d(co) = 125 mu m, and numerical aperture NA = 0.30 are inserted into a fluoroindate capillary with a lower refractive index. The whole structure is tapered down similar to 2.4 times the initial diameter for a waist length Lw = 21.6 mm to achieve power coupling between the two optical fibers. The device is characterized at the wavelength lambda = 3.34 mu m, employing an interband cascade laser pigtailed with a single-mode fluoroindate optical fiber. The 2x2 optical fiber coupler is characterized in terms of through port and cross port powers, showing perfect agreement with the numerical results. A coupling ratio CR = 48.1:51.9 is measured at the wavelength. = 3.34 mu m, with a reduced excess loss E-L < 1.2 dB. These results pave the way for reliable fabrication of high-performance fused optical fiber components that can boost research toward the development of all-in-fiber mid-infrared systems, such as in-band pumped mid-infrared amplifiers.