You were very nearly there, just add name path=W to the line drawing the water surface, and something like
\addplot [fill=blue!10] fill between[of=P and W];
right after it.
I'd suggest reducing the number of samples by a factor of about 100, from 5000 to 50 or 100. You don't need that may samples to plot a decent looking parabola, it only increases the time it takes to generate the figure.
\documentclass[tikz,11pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=newest}
\definecolor{mycolor}{RGB}{139,0,0}
\definecolor{water}{RGB}{123,158,200}
\begin{document}
\begin{tikzpicture}[/pgf/declare function={f=sin((x)r);}]
\begin{axis}
[restrict x to domain=-8:4, xmax=4, xmin=-8,
restrict y to domain=-1:5, ymax=5, ymin=-1,
x=1cm,
y=1cm,
hide y axis,
hide x axis,
samples=100,
>=stealth,]
\addplot [name path=P,line width=1,smooth,domain=-5.3:3.2] {0.25*x^2+0.5*x-0.25};
\draw[name path=W,decorate,decoration= {snake,amplitude=0.12mm},water,thick](axis cs:-4.4641,2.5)--(axis cs:2.4641,2.5);
\addplot [fill=blue!10] fill between[of=P and W];
\draw [thick,->](axis cs:-3,0)--(axis cs:3,0);
\draw [thick,->](axis cs:-2,-0.5)--(axis cs:-2,5);
\fill[mycolor](axis cs: -2,-0.25) rectangle (axis cs:-1.9,3.5);
\draw[thick,<->](axis cs:-3,0.5)--(axis cs:-2,0.5);
\draw[thick,<->](axis cs:-4,1.75)--(axis cs:-2,1.75);
\draw[thick,<->](axis cs:-5,3.5)--(axis cs:-2,3.5);
\node[above] at (axis cs:-3.5,3.5){3 m};
\node[above] at (axis cs:-3,1.75){2 m};
\node[above] at (axis cs:-2.5,0.5){1 m};
\node[right] at (axis cs:-2,0.2){\small O};
\node[left] at (axis cs:-3,0.5){A};
\node[left] at (axis cs:-4,1.75){N};
\node[left] at (axis cs:-5,3.5){M};
\node[right] at (axis cs:-1.9,0.5){0,5 m};
\node[right] at (axis cs:-1.9,1.75){1,75 m};
\node[right] at (axis cs:-1.9,3.5){3,5 m};
\node[right] at (axis cs:-1.9,2.8){Bâton};
\node[draw,anchor=west] at (axis cs:-7,0.5){Août};
\node[draw,anchor=west] at (axis cs:-7,1.75){Novembre};
\node[draw,anchor=west] at (axis cs:-7,3.5){Mars};
\node[anchor= east] at (axis cs:-3.1,0){Grande sécheresse};
\end{axis}
\end{tikzpicture}
\end{document}
Some simplifications
Here I shortened the code a bit. First of all, note that if you have compat=1.11 or newer, the axis cs coordinate system is default, so (axis cs:x,y) is the same as (x,y).
Second, note that when you draw a path from a to b, you can add nodes in the same path. So instead of adding the double arrow, the label above, the label to the left and the label to the right in four individual steps, you can do everything in once. The advantage of doing it like this is that you don't have to guess appropriate coordinates for the middle label, and if you need to change the position of the arrows at some point, there are fewer numbers to change.
Because many coordinates are on the parabola, I also defined a function for it, and used that for most y-coordinates. Again, doing things this way makes it easier should you want to change things.
\documentclass[tikz,11pt,border=5mm]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.13}
\definecolor{mycolor}{RGB}{139,0,0}
\definecolor{water}{RGB}{123,158,200}
\begin{document}
\begin{tikzpicture}[/pgf/declare function={f(\x)=0.25*\x^2+0.5*\x-0.25;}]
\begin{axis}
[restrict x to domain=-8:4, xmax=4, xmin=-8,
restrict y to domain=-1:5, ymax=5, ymin=-1,
x=1cm,
y=1cm,
hide y axis,
hide x axis,
samples=100,
>=stealth,]
\addplot [name path=P,line width=1,smooth,domain=-5.3:3.2] {f(x)};
\draw[name path=W,decorate,decoration={snake,amplitude=0.12mm},water,thick] (-4.4641,{f(-4.4641})--(2.4641,{f(2.4641)});
\addplot [fill=blue!10] fill between[of=P and W];
\draw [thick,->](-3,0)--(3,0);
\draw [thick,->](-2,-0.5)--(-2,5);
\fill[mycolor]( -2,-0.25) rectangle (-1.9,3.5);
\draw[thick,<->] (-3,{f(-3)}) node[left]{A} -- node[above] {1\,m} (-2,{f(-3)}) node[right=3pt]{0.5\,m};
\draw[thick,<->] (-4,{f(-4)}) node[left]{N} -- node[above] {2\,m} (-2,{f(-4)}) node[right=3pt]{1.75\,m};
\draw[thick,<->] (-5,{f(-5)}) node[left]{M} -- node[above] {3\,m} (-2,{f(-5)}) node[right=3pt]{3.5\,m};
\node[right] at (-2,0.2){\small O};
\node[right] at (-1.9,2.8){Bâton};
\node[draw,anchor=west] at (-7,{f(-3)}) {Août};
\node[draw,anchor=west] at (-7,{f(-4)}) {Novembre};
\node[draw,anchor=west] at (-7,{f(-5)}) {Mars};
\node[anchor=east] at (-3.1,0){Grande sécheresse};
\end{axis}
\end{tikzpicture}
\end{document}
