Vertical alignment of glyph

One can raise the ornaments using a \vcenter{\hbox{...}} approach. That way, the ornaments will be placed on the (implicit) math axis.

A couple of style-related comments: (i) If you provide this type of ornaments, I think you should use a font that uses old-style numerals -- at least for the page numbers. (ii) I'd also provide a bit more space between the ornaments and the page numbers, e.g., with the help of \quad statements. Otherwise, the page number block risks looking, well, too "blocky".

\documentclass{extreport}
\usepackage{pgfornament,cfr-lm}
\newcommand{\myraise}[1]{$\vcenter{\hbox{#1}}$}

\usepackage{fancyhdr}
\pagestyle{fancy}
\renewcommand{\headrulewidth}{0pt}
\fancyhead{}
\fancyfoot{}
\cfoot{\myraise{\pgfornament[scale=0.25]{11}}\quad%
       \thepage\quad\myraise{\pgfornament[scale=0.25]{14}}}

\begin{document}
\setcounter{page}{316}
\null % make sure document isn't entirely empty
\end{document}

---

Addendum: If you wish to use the cfr-lm font package while using oldstyle numerals only for the page numbers (and, hence, "lining" numerals everywhere else in the document), I suggest you add the following instructions to the preamble:

\usepackage[rm={lining,tabular},sf={lining,tabular},tt={lining,tabular}]{cfr-lm}
\renewcommand\thepage{\textpo{\arabic{page}}} 

That way, lining/tabular numerals will be the default everywhere except for page numbers, for which oldstyle/proportional numerals will be in use.

The ornament sits symmetrically on the baseline, which is good for deciding how much to raise it in your case.

Assuming you use lining figures, the amount of raising is exactly half the height of a figure in the current font.

\documentclass{article}
\usepackage{pgfornament}

\newcommand{\figureornament}[2][1]{%
  \raisebox{.5\fontcharht\font`0}{%
    \pgfornament[scale=#1]{#2}%
  }%
}

\begin{document}

\figureornament[0.25]{11} 317 \figureornament[0.25]{14}

\end{document}

It's immaterial whether you use that in \cfoot.

You can use the \raisebox command.

\raisebox{distance}[extend-above][extend-below]{text}

The \raisebox command is used to raise or lower text. The first mandatory argument specifies how high the text is to be raised (or lowered if it is a negative amount). The text itself is processed in LR mode.

Sometimes it's useful to make LaTeX think something has a different size than it really does - or a different size than LaTeX would normally think it has. The \raisebox command lets you tell LaTeX how tall it is.

The first optional argument, extend-above, makes LaTeX think that the text extends above the line by the amount specified. The second optional argument, extend-below, makes LaTeX think that the text extends below the line by the amount specified.

Source

In this case, wrap your \pgfornament command in a \raisebox, and adjust the distance value until it looks right. For example,

\raisebox{3pt}{\pgfornament[scale=0.25]{11}}