Full-field optical coherence microscopy (FFOCM) is an interferometric technique for obtaining wide-field microscopic images deep within scattering biological samples. FFOCM has primarily been implemented in the 0.8 mum wavelength range with silicon-based cameras, which may limit penetration when imaging human tissue. In this paper, we demonstrate FFOCM at the wavelength range of 0.9 - 1.4 mum, where optical penetration into tissue is presumably greater owing to decreased scattering. Our FFOCM system, comprising a broadband spatially incoherent light source, a Linnik interferometer, and an InGaAs area scan camera, provided a detection sensitivity of 86 dB for a 2 sec imaging time and an axial resolution of 1.9 mum in water. Images of phantoms, tissue samples, and Xenopus Laevis embryos were obtained using InGaAs and silicon camera FFOCM systems, demonstrating enhanced imaging penetration at longer wavelengths.