Also, keep in mind you change the [color=#000000][font=Times][size=1]glPolygonMode to [/font][color=#000000][font=monospace][size=1]GL_LINE[/font][color=#000000][font=Times][size=1] and then you might not have to write a whole bunch of new rendering code. [/font]

A VBO is not likely to help so much here as your data looks to be dynamic and your code is nasty - see further down for help with this; you certainly won't see jumps from 15fps to 60 or more (immediate mode is slow but it's not that slow). I really wish people would stop recommending "use a VBO" as if it's some kind of magic dust that you can just sprinkle on bad or slow code to make it good or fast - it's not.

There are a few things in your code that are hurting you and that you can fix Right Now. VBO or no VBO, these are your primary problems and need to be addressed.

glLineWidth (2.0) - values other than 1 may not be hardware accelerated. Try setting it to 1, if performance jumps dramatically then it's a reasonably decent indication that your driver is falling back on some form of software emulation (perhaps faking lines by using solid quads, perhaps something else).

I expect it won't jump because of...

State changes. The way you're handling these is almost a textbook case of the worst possible way to do it (sorry, but it's true). You've a whole heap of state changes inside of a loop that could easily be moved outside of it, you've a glPushMatrix and glPopMatrix that do absolutely nothing at all (since you don't do any transforms between them) - again inside of the same loop, and you've a second inner glBegin/glEnd pair inside of your first glBegin/glEnd pair (GL_LINE isn't even a valid param for glBegin).

Your drawline function could and should be reduced to this:
void DrawLine(GLpoint a, GLpoint b, float R, float G, float B)
{
glColor3f(R, G, B);
glVertex3f(a.x, a.y, a.z);
glVertex3f(b.x, b.y, b.z);
}
The state changes go outside the for loop in RenderModelMeshAsLines, which then looks like this:
void RenderModelMeshAsLines (GLpoint *P, GLFace *T, int nbF)
{
if (nbF > 0)
{
GLfloat r = 0.0f, g = 0.0f, b = 0.0f;

glLineWidth (2.0);
glPushAttrib (GL_CURRENT_BIT | GL_ENABLE_BIT | GL_LIGHTING_BIT | GL_LINE_BIT);

glDisable (GL_LIGHTING);
glEnable (GL_LINE_SMOOTH);
glHint (GL_LINE_SMOOTH_HINT, GL_NICEST);
glEnable (GL_BLEND);
glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
glBegin (GL_LINES);

for (int i = 0; i < nbF; i++)
{
DrawLine (P[T.v1], P[T.v2], r, g, b);
DrawLine (P[T.v2], P[T.v3], r, g, b);
DrawLine (P[T.v3], P[T.v1], r, g, b);
}

glEnd ();
glPopAttrib ();
glLineWidth (1.0);
}
}
Just this basic clean-up and correction should be enough to see your performance go back up to where you want it to be. If it's still not enough then look at VBOs or geometry shaders, but not before. Correct your code and get it well-behaving first.