Will a 2003 Renault Clio 1.5dci engine fit into a 2001 Renualt Clio 1.5dci?

Yes it will, 1.5 dci was mounted in Clio II ph2, and as pH 2 was facelifting without any major changes in construction it should fit without any problems (using parts from pH 2 clio). It may be possible to even fit 1.9 dci engines as non-turbo 1.9 was mounted in clio before 1.5dci was introduced.