PRESENT PARTICIPLE

I.  As in English, French uses the past participle to create nouns ("le participant"/"the participant"); adjectives ("intéressant"/"interesting"); and prepositions ("durant"/"during").  You need only memorize these case by case.

II.  French uses the present participle  in its verbal form much less frequently than does English. Often the English present participle is replaced by a French infinitive, relative clause, or simple tense: 

Examples:
(infinitive): I saw her working:  Je l'ai vu travailler.
(relative clause):  I saw him leaving:  Je l'ai vu qui partait.
(simple tense):  I am calling:  J'appelle; He was coming:  Il venait; They will be eating:  Ils mangeront.

III.  French does use the present participle in its verbal form in very specific cases:

A.  "En" + Present Participle.  

"En" + present participle signifies an action that is both: 
a.  performed by the subject of the main verb and
b. simultaneous with the action signified by the main verb.

1.  "En + Present Participle"  may express mere simultaneity, what the subject is doing "WHILE" he is doing something else:

Example:
Elle est partie en parlant à son ami.
(The acts of leaving and speaking take place at the same time and are performed by the subject of the sentence, "elle."  She left "while" talking to her friend.)

2.  "En + Present Participle" may signify a simultaneous action that expresses "WHEN" the main action is performed:

Example:
Il lisait un livre en entrant dans le metro. (When was he reading a book?  When he was entry the subway).

3.  "En + Present Participle" may also signify a simultaneous action that expresses "HOW" the main action is performed, in other words the "WAY IN WHICH" it is performed or the "MEANS BY WHICH": it is performed.

Examples:
Je laverai la voiture en la frottant très fort.
How did we succeed in cleaning the car? By what means? By rubbing very hard
Elle passait en pleurant.
How did she pass by?  In what way or manner?  Crying.

4. "Tout en" + present participle is used to suggest that the simultaneity of two actions is unexpected,  difficult, or contradictory.   The subject does something "EVEN WHILE" something else.

Examples:
Tout en regardant la télé, elle faisait ses devoirs.
Tout en niant la vérité, il l'affirmait par son rougissement.

B.  Present Participle (without "en") (used in less familiar, more formal discourse)

1.  The present participle alone can be used to express a relationship of sequentiality (anteriority or posteriority) between actions performed by the subject of the sentence.  The sequential relationship may also represent a logical relationship between cause and effect, reason and action, action and result.

a.   Mere anteriority (before) or posteriority (after):

Examples:
Prenant son chapeau, il est parti.
He first took his hat, then he left.
Il a laissé tomber une allumette, produisant un incendie.
He dropped a match, producing (after) a fire.

b.   Logical anteriority (before) or posteriority (after):

Examples:
Pensant qu'il n'en aurait pas besoin, elle a pris la voiture.
Thinking (reason) that he would not need it, she took the car (action). 
Il est tombé par terre, se cassant la jambe.
He fell (cause) and broke his leg (effect).

c.   The sequential relationship may be partial (one action precedes the other, but continues on after the other starts) or total (one action ends before the next begins).  In order to make it absolutely clear that one action precedes, but does not overlap, the other, use the compound form of the present participle: 
Present Participle of the auxiliary + Past Participle of the verb.

Examples:
Overlap:  Pensant qu'il n'en aurait pas besoin, elle a pris la voiture.
Thinking that he would not need it, she took the car.  The thinking began before but also continued after she took the car.
No Overlap:  Ayant réfléchi toute la journée, il s'est résolu à lui dire la vérité.
He thought the entire day, then, having finished his thinking, he made his resolution.

2. The present participle alone can, in very specific cases, be used to express a relationship of simultaneity.  These cases should be carefully distinguished from those in which "en + present participle" is used:

a. A simultaneous action performed by the direct object of the sentence.

Example:
Elle l'a entendu entrer riant follement. 
We heard him (the direct object) enter laughing madly.
(vs. Elle l'a écouté en riant follement. She (the subject) is laughing madly.)

b. A simultaneous action performed by the subject of the sentence that constitutes a mere circumstance accompanying the action signified by the main verb (not a cause, an effect, a reason, or a result).

Example:
Elle est entrée chez elle pensant au bal.
The subject performs the actions of entering and thinking at the same time, but the simultaneity of the two actions is not stressed.  They just happen to coincide.  
(vs. Elle est entrée en pensant au bal. The "en" stresses the simultaneity and suggests that the thinking describes the manner in which she entered).

3.  A present participle alone, whether it expresses a sequential action (B.1.) or a simultaneous action (B.2.), often replaces a relative clause, particularly in everyday speach.  

Example:
Jean, reconnaissant (qui reconnaissait) qu'il avait gagné, est tombé par terre (sequentiality).
Il l'a vue partir pleurant sa mère.  Il l'a vue partir qui pleurait sa mère. (simultaneity).