Are all the other standard French accent keys working as you would expect? For example Lower case (7è 9ç 0à 2é) Alt-Gr-a æ Alt-Gr-q @ etc. In other words it is just the sticky keys that are giving you the problem or all the French accents.
Have you installed the French Language package or are you just using the default Eng-US?
And the Language settings are set to French?
Tools > Options > Language settings > French
It is also worth looking to make certain that the Autocorrect function is not overwriting your text. Tools > Autocorrect options.
As a temporary help, not a solution, I have used the French spellcheck to correct the missing accents. (French is not my native language)
What version of LibreOffice are you using? I can’t reproduce your problem using LibO 3.6.4, 4.0.1 on Ubuntu 12.04 with a UK, French-French or Swiss-French keyboard. Sorry not to be more help.