A fan vane for a turbomachine, such as an aircraft turbojet or turboprop, the vane (12', 12') having an upstream side and a downstream side and having, in a radial direction of elongation of the vane: - a blade (13',13") having a leading edge along the upstream side and a trailing edge along the downstream side, - a root (18',18") to be engaged in a groove of a disc of the turbomachine, the root being located radially further inside than the blade and having upstream and downstream ends, transversely to said radial direction of elongation, - an inner inter-vane platform located radially between the root (18',18") and the blade (13',13"), on which vane, an upstream end (450',450") of the root connects to a radially inner end of the leading edge (431',431") of the blade by an upstream edge of a connecting zone (47',47") which: -- is radially intermediate between the root (18',18") and the inner inter-vane platform (16',16",16a"), and -- has a recess towards the downstream (49',49"), such that said radially inner end (430', 430") of the leading edge of the blade is located further downstream than the upstream end of the root, the upstream edge of said connecting zone (47', 47") having a concave shape which advances upstream from the blade towards the root, and the downstream edge of said connecting zone (47', 47") having a concave shape and/or which moves back downstream, from the blade towards the root, characterised in that: - the leading edge (431', 431") and the trailing edge (457', 457") of the blade connect to said platform (16', 16", 16a"), each at a radially inner end, by a concave shape (433', 433"; 432'), - radially outwardly, beyond the concave shape (433', 433"), the leading edge (431',431") and the trailing edge (457', 457") of the blade each have a convex shape, and - the convex shape of the leading edge (453', 453") of the blade is more rounded than that (459', 459") of the trailing edge of the blade. - a blade (13',13") having a leading edge along the upstream side and a trailing edge along the downstream side, - a root (18',18") to be engaged in a groove of a disc of the turbomachine, the root being located radially further inside than the blade and having upstream and downstream ends, transversely to said radial direction of elongation, - an inner inter-vane platform located radially between the root (18',18") and the blade (13',13"), on which vane, an upstream end (450',450") of the root connects to a radially inner end of the leading edge (431',431") of the blade by an upstream edge of a connecting zone (47',47") which: -- is radially intermediate between the root (18',18") and the inner inter-vane platform (16',16",16a"), and -- has a recess towards the downstream (49',49"), -- is radially intermediate between the root (18',18") and the inner inter-vane platform (16',16",16a"), and -- has a recess towards the downstream (49',49"), such that said radially inner end (430', 430") of the leading edge of the blade is located further downstream than the upstream end of the root, the upstream edge of said connecting zone (47', 47") having a concave shape which advances upstream from the blade towards the root, and the downstream edge of said connecting zone (47', 47") having a concave shape and/or which moves back downstream, from the blade towards the root, characterised in that: - the leading edge (431', 431") and the trailing edge (457', 457") of the blade connect to said platform (16', 16", 16a"), each at a radially inner end, by a concave shape (433', 433"; 432'), - radially outwardly, beyond the concave shape (433', 433"), the leading edge (431',431") and the trailing edge (457', 457") of the blade each have a convex shape, and - the convex shape of the leading edge (453', 453") of the blade is more rounded than that (459', 459") of the trailing edge of the blade. - the leading edge (431', 431") and the trailing edge (457', 457") of the blade connect to said platform (16', 16", 16a"), each at a radially inner end, by a concave shape (433', 433"; 432'), - radially outwardly, beyond the concave shape (433', 433"), the leading edge (431',431") and the trailing edge (457', 457") of the blade each have a convex shape, and - the convex shape of the leading edge (453', 453") of the blade is more rounded than that (459', 459") of the trailing edge of the blade.