I had never heard of a dangling participle and wouldn’t have thought I’d learn about such a fine grammatical point while subtitling an episode of American Dreams, but there you go. A dangling participle is a participle that doesn’t modify the subject of a sentence.
Example:
Trying to meet my Friday deadline, my pc suddenly decided to stop working.
Dangling participles are fairly common but it’s best to avoid them in English; indeed, their freedom of movement can make a sentence very ambiguous. Example:
Riding down the street on my bicycle, a dog knocked me over.
Who’s riding the bicycle? The dog?
The above two examples could be rephrased in the following manner:
As I was trying to meet my deadline, my pc suddenly decided to stop working.
As I was riding down the street on my bicycle, a dog knocked me over.

In French, the same rule applies, but it is definitely not as strict, and the épithète détachée much less offensive.