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One of my favorite poets is probably Guillaume Apollinaire. His story and proximity to Picasso made him a precursor. Calligrams was a constant attempt to merge poetry and visual. I am wondering how we could actually recreate in TikZ

This is just to mention that TikZ has already built in a large selection of tricks that can be applied to paths. Here is a very basic example. (Yes, I know I am not a poet.;-)

documentclass[tikz,border=3.14mm]standalone
usetikzlibrarydecorations.text
begindocument
begintikzpicture
defmypath
 (-2,0) to[bend right=10] (0,5.1)
 to[bend right=10] (2,0) -- (1.5,0) -- (0.8,1) -- (-0.8,1) -- (-1.5,0) -- cycle
draw mypath; 
path[decorate,decoration=text along path,
text=In Paris there is a tower and beneath it there grows a flower. And often
on Mondays there is a shower.] mypath;
endtikzpicture
enddocument

The IMHO most stunning tools are however not from the pgfmanual, but due to Paul Gaborit's great answer. You basically define the contour and the macro takes care of the rest. (Of course, you may want to tune things in the end a bit, but it is stunning how much it does out of the box.)

documentclassstandalone
usepackagelmodern
usepackage[T1]fontenc
usepackageshapepar
usepackagemicrotype
usepackagelipsum
usepackagetikz
usetikzlibrarycalc,fit,intersections

defshapeparnodeaccuracy2
newcommandshapeparnode[6][] xmin pt,0)
 Shapepar[1pt]boundshape#6par;


defmytextIn Paris there is a tower and beneath it there grows a flower.

begindocument%
 begintikzpicture
 defpathone(0,1) -- (-0.8,1) -- (-1.5,0) --
 (-2,0) to[bend right=10] (0,5.1)
 defpathtwo(0,5.1)
 to[bend right=10] (2,0) -- (1.5,0) -- (0.8,1) -- (-0.8,1)
 fill[top color=lime,bottom color=orange,middle color=yellow,draw=white]
 pathone -- pathtwo -- cycle;
 defpathone(0,1) -- (-0.8,1) -- (-1.5,0) --
 (-1.6,0) to[bend right=10] (0,4.1)
 defpathtwo(0,4.1)
 to[bend right=10] (1.6,0) -- (1.5,0) -- (0.8,1) -- (-0.8,1)
 shapeparnode[text=black,font=footnotesizescshape]
 0.1em0.1empathonepathtwomytext%
 %draw[orange] pathone;
 %draw[orange] pathtwo;
endtikzpicture
enddocument