ï & î font encoding

With LuaTeX the glyph isn't available for Garamond Regular. I tried it with the Garamond Pro and Garamond Premier Pro. Only the italic and bold variant show the character. But EBGaramond has it:

If I run the example with xelatex instead of lualatex then everything is fine with AGaramondPro, too:

As Enrico said, use another font if you do not have the EBGaramond, at least for the bibliography. However, you can write your bibliography with unicode characters:

@book{GoncalvesdaCosta:2000tw,
author = {Goncalves Da Costa, Héloïsea},
title = {Les musées d'histoire de ville leur contribution au développement social contemporain.},
publisher = {Université du Québec à Montréal},
year = {2000},
address = {Montréal}}

Biber can handle all that.

Short answer

Biber does not understand {\"\i}. Fix the encoding with recode:

recode -d latex..UTF-8 biblio.bib 

Too long answer

The problem seems to be the string {\"\i} (which is meant to represent ï) in your bibliography. Biber gets confused and interprets it as {\"ı}, which is nonsense, and in turn, responsible for the bad output.

So the question is, what to do with the offending character? There are two general answers:

1. Change the way your bibliography gets processed
2. Remove the offending string from your bibliography

1. Change how the bibliography is processed

1.1 Call biber with --output_safechars.

To force biber to pass {\"\i} along unchanged, and thus getting the correct output, simply use the option --output_safechars:

xelatex document
biber --output_safechars document
xelatex document
xelatex document

1.2. Use bibtex8 as backend.

BibTeX does not modify {\"\i} in the process and it can be used with 'BibLaTeX'. (It is possible but not recommended using BibTeX instead of biber, because a lot of the advanced features will work only with the latter.) To do so set the option backend=bibtex8. Your MWE would look like this:

% !TEX encoding = UTF-8 Unicode
\documentclass[12pt]{scrbook}

\usepackage[english,frenchb]{babel}             
\usepackage[quiet]{fontspec}    

\usepackage[automark]{scrpage2}
\usepackage[babel,french=guillemets*]{csquotes} 
\usepackage[backend=bibtex8,style=authortitle-ticomp,doi=false]{biblatex} % <-- changed backend

\frenchbsetup{FrenchFootnotes=false}
\MakeOuterQuote{"}

\setmainfont[Mapping=tex-text, Ligatures={Common, Rare}, Numbers={OldStyle}]{Adobe Garamond Pro}

\addtokomafont{disposition}{\normalfont}
\addtokomafont{pageheadfoot}{\normalfont}       
\addtokomafont{pagenumber}{\normalfont} 
\addtokomafont{footnote}{\normalfont}               
\addtokomafont{footnotereference}{\normalfont}

\addbibresource{biblio.bib}             
\AtBeginBibliography{\def\UrlFont{\scriptsize}}

\begin{document}
"Héloïse"\footcite{GoncalvesdaCosta:2000tw}.
\printbibliography
\end{document}

To compile the document call:

xelatex document
bibtex document
xelatex document
xelatex document 

Both ways produce PDFs with correctly rendered ï:

2. Prevent {\"\i} from ending up in bibliography

2.1. Change the exported bibliography

The general approach would be replacing all occurrences of \"\i in your bibliography with \"i. This could be done with any text editor capable of searching and replacing strings. Of course there are tools to do that for you. sed is one of them:

sed s/\\"\\i/\\"i/g  < in.bib > out.bib 

Don't worry, there are others beside sed. The best tool on the command line is of course recode, all you have to do is:

recode -d latex..UTF-8 biblio.bib 

(Unfortunately recode does not come preinstalled with Mac OS X, but it can be easily installed with Homebrew.)

As you are on a Mac, you could use BibDesk:

1. Open your bibliography with BibDesk:

2. Export (Menu --> File --> Export...) as BibTeX and Unicode (UTF-8):

This will provide you with a valid UTF-8 BibLaTeX compatible file:

%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/


%% Created for you at 2014-02-11 23:42:00 +0000 


%% Saved with string encoding Unicode (UTF-8) 



@book{GoncalvesdaCosta:2000tw,
    Address = {Montréal},
    Author = {Goncalves Da Costa, Héloïsa},
    Publisher = {Université du Québec à Montréal},
    Title = {{Les musées d'histoire de ville leur contribution au développement social contemporain.}},
    Year = {2000}}

2.2. Use software capable of exporting BibLaTeX

Maybe you should ditch Papers and switch to JabRef, BibDesk, Mendeley, Zotero, vim or emacs.