Can the employer fire the employee because they are planning to take
FMLA later?
No.
Firing someone or taking other job related retaliation for taking or planning to take FMLA leave is illegal:
Section 105 of the FMLA and section 825.220 of the FMLA regulations
prohibit the following actions:
An employer is prohibited from interfering with, restraining, or denying the exercise of, or the attempt to exercise, any FMLA right.
An employer is prohibited from discriminating or retaliating against an employee or prospective employee for having exercised or attempted
to exercise any FMLA right.
An employer is prohibited from discharging or in any other way discriminating against any person, whether or not an employee, for
opposing or complaining about any unlawful practice under the FMLA.
All persons, whether or not employers, are prohibited from discharging or in any other way discriminating against any person,
whether or not an employee, because that person has —
Filed any charge, has instituted, or caused to be instituted, any proceeding under or related to the FMLA;
Given, or is about to give, any information in connection with an inquiry or proceeding relating to any right under the FMLA; or
Testified, or is about to testify, in any inquiry or proceeding relating to a right under the FMLA.
Examples of prohibited conduct include:
Refusing to authorize FMLA leave for an eligible employee,
Discouraging an employee from using FMLA leave,
Manipulating an employee’s work hours to avoid responsibilities under the FMLA,
Using an employee’s request for or use of FMLA leave as a negative factor in employment actions, such as hiring, promotions, or
disciplinary actions, or,
Counting FMLA leave under “no fault” attendance policies.
Any violations of the FMLA or the Department’s regulations constitute
interfering with, restraining, or denying the exercise of rights
provided by the FMLA.
This conduct is clearly not allowed.
What protections exist for the employee in this situation?
The employee can file a complaint with the U.S. Department of Labor. If the employer does not reach a settlement with the U.S. Department of Labor, the government can sue, and if the government fails to sue, the individual can sue. The remedy, if the employee prevails (directly or through the Department of Labor), will generally be a judgment for money damages against the employer rather than the reinstatement of the employee to their job.
As explained at the link above:
The Wage and Hour Division administers and enforces the FMLA for all
private, state and local government employees, and some federal
employees. The Wage and Hour Division investigates complaints. If
violations cannot be satisfactorily resolved, the U.S. Department of
Labor may bring action in court to compel compliance. An employee may
also be able to bring a private civil action against an employer for
violations. In general, any allegation must be raised within two years
from the date of violation.
It is worth noting that while the FMLA violation deadline is two years, for most federal employment discrimination lawsuits, an EEOC complaint was be filed within six months of the discriminatory act.
The "going rate" for settlements of wrongful termination cases like this one has historically been a settlement payment of about six months of pay at the job an employee was wrongfully fired from, as a reflection of the length of time it takes a reasonable person who was wrongfully fired to find a new job. Of course, some cases are stronger in terms of liability and damages, and some cases are weaker.
In bigger businesses (or in the case of unionized workers), it also wouldn't be unprecedented for there to be an early settlement reinstating someone to their job, even though a court can't order that remedy.
Private attorneys who handle these kinds of cases would typically describe themselves as "employment lawyers" and would typically work as sole practitioners or in small or medium sized law firms. Large law firms typically have a policy of only representing employers or employees who are senior executives.
Is it much harder to prove that the termination was a consequence of
the planned FMLA?
Basically, if it is possible that the employee could have been fired for FMLA related reasons, the burden is on the employer to show that there was another reason for doing so, and the judge or jury, as the case may be can consider all admissible evidence to determine if the firing for a claimed non-FMLA reason was sincere or was a pre-text for an improper FMLA related reason for firing someone.
How hard it is to prove a FMLA violation in a particular case varies widely. It depends upon what witness testimony and documentation can be located by each side of the case. It is a crime to give false testimony in a court case, but, of course, that doesn't mean that it doesn't ever happen.
UPDATE: The U.S. Supreme Court today weakened the standard of proof that must be established to win a retaliation lawsuit under a whistleblower retaliation statute. This standard will probably be applied to FMLA cases as well. It held that:
A whistleblower who invokes §1514A must prove that his protected
activity was a contributing factor in the employer’s unfavorable
personnel action, but need not prove that his employer acted with
“retaliatory intent.”